Weight Multiplicities

Groups of type C8, degree bound 10000

Diagram:

1 > 2 - .. - 8

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: all
Dimension: 1

Level	dominant weight	weight multiplicity	length of W-orbit
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	1	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: all
Dimension: 16

Level	dominant weight	weight multiplicity	length of W-orbit
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	1	16

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 118

Level	dominant weight	weight multiplicity	length of W-orbit
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	1	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	6	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: not 2
Dimension: 119

Level	dominant weight	weight multiplicity	length of W-orbit
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	1	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	7	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2
Dimension: 136

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 0, 0, 0, 0, 0, 2 ]	1	16
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	1	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	8	1

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 256

Level	dominant weight	weight multiplicity	length of W-orbit
65	[ 1, 0, 0, 0, 0, 0, 0, 0 ]	1	256

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: 7
Dimension: 528

Level	dominant weight	weight multiplicity	length of W-orbit
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	1	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	5	16

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: not 7
Dimension: 544

Level	dominant weight	weight multiplicity	length of W-orbit
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	1	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	6	16

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 800

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 0, 0, 0, 0, 0, 0, 1, 1 ]	1	224
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	1	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	8	16

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3
Dimension: 816

Level	dominant weight	weight multiplicity	length of W-orbit
46	[ 0, 0, 0, 0, 0, 0, 0, 3 ]	1	16
44	[ 0, 0, 0, 0, 0, 0, 1, 1 ]	1	224
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	1	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	8	16

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 17
Dimension: 1328

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 0, 0, 0, 0, 0, 0, 1, 1 ]	1	224
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	2	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	13	16

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 3,17
Dimension: 1344

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 0, 0, 0, 0, 0, 0, 1, 1 ]	1	224
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	2	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	14	16

Highest weight: [ 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: 3
Dimension: 1581

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	1	1120
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	4	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	13	1

Highest weight: [ 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 1582

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	1	1120
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	4	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	14	1

Highest weight: [ 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: 7
Dimension: 1699

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	1	1120
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	5	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	19	1

Highest weight: [ 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: not 2,3,7
Dimension: 1700

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	1	1120
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	5	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	20	1

Highest weight: [ 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 5
Dimension: 3264

Level	dominant weight	weight multiplicity	length of W-orbit
56	[ 0, 0, 0, 1, 0, 0, 0, 0 ]	1	1792
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	3	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	8	16

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 3280

Level	dominant weight	weight multiplicity	length of W-orbit
64	[ 0, 1, 0, 0, 0, 0, 0, 0 ]	1	1024
56	[ 0, 0, 0, 1, 0, 0, 0, 0 ]	1	1792
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	1	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	1	16

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 3281

Level	dominant weight	weight multiplicity	length of W-orbit
65	[ 1, 0, 0, 0, 0, 0, 0, 0 ]	1	256
61	[ 0, 0, 1, 0, 0, 0, 0, 0 ]	1	1792
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	1	1120
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	1	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	1	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 3620

Level	dominant weight	weight multiplicity	length of W-orbit
57	[ 0, 0, 0, 0, 0, 0, 2, 0 ]	1	112
55	[ 0, 0, 0, 0, 0, 1, 0, 1 ]	1	1344
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	1	1120
31	[ 0, 0, 0, 0, 0, 0, 0, 2 ]	7	16
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	8	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	36	1

Highest weight: [ 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 3792

Level	dominant weight	weight multiplicity	length of W-orbit
56	[ 0, 0, 0, 1, 0, 0, 0, 0 ]	1	1792
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	4	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	13	16

Highest weight: [ 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: not 3,5
Dimension: 3808

Level	dominant weight	weight multiplicity	length of W-orbit
56	[ 0, 0, 0, 1, 0, 0, 0, 0 ]	1	1792
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	4	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	14	16

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3
Dimension: 3876

Level	dominant weight	weight multiplicity	length of W-orbit
61	[ 0, 0, 0, 0, 0, 0, 0, 4 ]	1	16
59	[ 0, 0, 0, 0, 0, 0, 1, 2 ]	1	224
57	[ 0, 0, 0, 0, 0, 0, 2, 0 ]	1	112
55	[ 0, 0, 0, 0, 0, 1, 0, 1 ]	1	1344
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	1	1120
31	[ 0, 0, 0, 0, 0, 0, 0, 2 ]	8	16
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	8	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	36	1

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 4096

Level	dominant weight	weight multiplicity	length of W-orbit
80	[ 1, 0, 0, 0, 0, 0, 0, 1 ]	1	2048
64	[ 0, 1, 0, 0, 0, 0, 0, 0 ]	2	1024

Highest weight: [ 0, 0, 1, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 4488

Level	dominant weight	weight multiplicity	length of W-orbit
61	[ 0, 0, 1, 0, 0, 0, 0, 0 ]	1	1792
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	2	1120
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	4	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	8	1

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: 5
Dimension: 4861

Level	dominant weight	weight multiplicity	length of W-orbit
65	[ 1, 0, 0, 0, 0, 0, 0, 0 ]	1	256
61	[ 0, 0, 1, 0, 0, 0, 0, 0 ]	1	1792
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	2	1120
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	5	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	13	1

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: not 2,3,5
Dimension: 4862

Level	dominant weight	weight multiplicity	length of W-orbit
65	[ 1, 0, 0, 0, 0, 0, 0, 0 ]	1	256
61	[ 0, 0, 1, 0, 0, 0, 0, 0 ]	1	1792
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	2	1120
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	5	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	14	1

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 5066

Level	dominant weight	weight multiplicity	length of W-orbit
55	[ 0, 0, 0, 0, 0, 1, 0, 1 ]	1	1344
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	2	1120
31	[ 0, 0, 0, 0, 0, 0, 0, 2 ]	6	16
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	12	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	42	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 17
Dimension: 5319

Level	dominant weight	weight multiplicity	length of W-orbit
57	[ 0, 0, 0, 0, 0, 0, 2, 0 ]	1	112
55	[ 0, 0, 0, 0, 0, 1, 0, 1 ]	1	1344
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	2	1120
31	[ 0, 0, 0, 0, 0, 0, 0, 2 ]	7	16
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	13	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	55	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,17
Dimension: 5320

Level	dominant weight	weight multiplicity	length of W-orbit
57	[ 0, 0, 0, 0, 0, 0, 2, 0 ]	1	112
55	[ 0, 0, 0, 0, 0, 1, 0, 1 ]	1	1344
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	2	1120
31	[ 0, 0, 0, 0, 0, 0, 0, 2 ]	7	16
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	13	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	56	1

Highest weight: [ 0, 0, 1, 0, 0, 0, 0, 0 ]
Characteristic: 5
Dimension: 6069

Level	dominant weight	weight multiplicity	length of W-orbit
61	[ 0, 0, 1, 0, 0, 0, 0, 0 ]	1	1792
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	3	1120
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	8	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	21	1

Highest weight: [ 0, 0, 1, 0, 0, 0, 0, 0 ]
Characteristic: not 2,5
Dimension: 6188

Level	dominant weight	weight multiplicity	length of W-orbit
61	[ 0, 0, 1, 0, 0, 0, 0, 0 ]	1	1792
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	3	1120
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	9	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	28	1

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 6528

Level	dominant weight	weight multiplicity	length of W-orbit
64	[ 0, 1, 0, 0, 0, 0, 0, 0 ]	1	1024
56	[ 0, 0, 0, 1, 0, 0, 0, 0 ]	2	1792
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	4	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	8	16

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: 7
Dimension: 6749

Level	dominant weight	weight multiplicity	length of W-orbit
55	[ 0, 0, 0, 0, 0, 1, 0, 1 ]	1	1344
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	3	1120
31	[ 0, 0, 0, 0, 0, 0, 0, 2 ]	5	16
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	17	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	61	1

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: not 2,7
Dimension: 6885

Level	dominant weight	weight multiplicity	length of W-orbit
55	[ 0, 0, 0, 0, 0, 1, 0, 1 ]	1	1344
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	3	1120
31	[ 0, 0, 0, 0, 0, 0, 0, 2 ]	6	16
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	18	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	69	1

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: 5
Dimension: 7056

Level	dominant weight	weight multiplicity	length of W-orbit
64	[ 0, 1, 0, 0, 0, 0, 0, 0 ]	1	1024
56	[ 0, 0, 0, 1, 0, 0, 0, 0 ]	2	1792
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	5	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	13	16

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: not 2,3,5
Dimension: 7072

Level	dominant weight	weight multiplicity	length of W-orbit
64	[ 0, 1, 0, 0, 0, 0, 0, 0 ]	1	1024
56	[ 0, 0, 0, 1, 0, 0, 0, 0 ]	2	1792
40	[ 0, 0, 0, 0, 0, 1, 0, 0 ]	5	448
16	[ 0, 0, 0, 0, 0, 0, 0, 1 ]	14	16

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 2 ]
Characteristic: 3
Dimension: 8908

Level	dominant weight	weight multiplicity	length of W-orbit
59	[ 0, 0, 0, 0, 0, 0, 1, 2 ]	1	224
57	[ 0, 0, 0, 0, 0, 0, 2, 0 ]	1	112
55	[ 0, 0, 0, 0, 0, 1, 0, 1 ]	2	1344
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	3	1120
31	[ 0, 0, 0, 0, 0, 0, 0, 2 ]	13	16
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	20	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	76	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 2 ]
Characteristic: not 2,3
Dimension: 9044

Level	dominant weight	weight multiplicity	length of W-orbit
59	[ 0, 0, 0, 0, 0, 0, 1, 2 ]	1	224
57	[ 0, 0, 0, 0, 0, 0, 2, 0 ]	1	112
55	[ 0, 0, 0, 0, 0, 1, 0, 1 ]	2	1344
49	[ 0, 0, 0, 0, 1, 0, 0, 0 ]	3	1120
31	[ 0, 0, 0, 0, 0, 0, 0, 2 ]	14	16
29	[ 0, 0, 0, 0, 0, 0, 1, 0 ]	21	112
1	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	84	1