Weight Multiplicities

Groups of type C7, degree bound 6000

Diagram:

1 > 2 - .. - 7

Highest weight: [ 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 ]	1	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: all
Dimension: 14

Level	dominant weight	weight multiplicity	length of W-orbit
14	[ 0, 0, 0, 0, 0, 0, 1 ]	1	14

Highest weight: [ 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 7
Dimension: 89

Level	dominant weight	weight multiplicity	length of W-orbit
25	[ 0, 0, 0, 0, 0, 1, 0 ]	1	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	5	1

Highest weight: [ 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: not 7
Dimension: 90

Level	dominant weight	weight multiplicity	length of W-orbit
25	[ 0, 0, 0, 0, 0, 1, 0 ]	1	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	6	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2
Dimension: 105

Level	dominant weight	weight multiplicity	length of W-orbit
27	[ 0, 0, 0, 0, 0, 0, 2 ]	1	14
25	[ 0, 0, 0, 0, 0, 1, 0 ]	1	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	7	1

Highest weight: [ 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 128

Level	dominant weight	weight multiplicity	length of W-orbit
50	[ 1, 0, 0, 0, 0, 0, 0 ]	1	128

Highest weight: [ 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 336

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 0, 0, 0, 0, 1, 0, 0 ]	1	280
14	[ 0, 0, 0, 0, 0, 0, 1 ]	4	14

Highest weight: [ 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: 3
Dimension: 336

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 0, 0, 0, 0, 1, 0, 0 ]	1	280
14	[ 0, 0, 0, 0, 0, 0, 1 ]	4	14

Highest weight: [ 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: not 2,3
Dimension: 350

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 0, 0, 0, 0, 1, 0, 0 ]	1	280
14	[ 0, 0, 0, 0, 0, 0, 1 ]	5	14

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 546

Level	dominant weight	weight multiplicity	length of W-orbit
38	[ 0, 0, 0, 0, 0, 1, 1 ]	1	168
34	[ 0, 0, 0, 0, 1, 0, 0 ]	1	280
14	[ 0, 0, 0, 0, 0, 0, 1 ]	7	14

Highest weight: [ 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3
Dimension: 560

Level	dominant weight	weight multiplicity	length of W-orbit
40	[ 0, 0, 0, 0, 0, 0, 3 ]	1	14
38	[ 0, 0, 0, 0, 0, 1, 1 ]	1	168
34	[ 0, 0, 0, 0, 1, 0, 0 ]	1	280
14	[ 0, 0, 0, 0, 0, 0, 1 ]	7	14

Highest weight: [ 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: 5
Dimension: 820

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 0, 0, 1, 0, 0, 0 ]	1	560
25	[ 0, 0, 0, 0, 0, 1, 0 ]	3	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	8	1

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 5
Dimension: 882

Level	dominant weight	weight multiplicity	length of W-orbit
38	[ 0, 0, 0, 0, 0, 1, 1 ]	1	168
34	[ 0, 0, 0, 0, 1, 0, 0 ]	2	280
14	[ 0, 0, 0, 0, 0, 0, 1 ]	11	14

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 3,5
Dimension: 896

Level	dominant weight	weight multiplicity	length of W-orbit
38	[ 0, 0, 0, 0, 0, 1, 1 ]	1	168
34	[ 0, 0, 0, 0, 1, 0, 0 ]	2	280
14	[ 0, 0, 0, 0, 0, 0, 1 ]	12	14

Highest weight: [ 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: 3
Dimension: 909

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 0, 0, 1, 0, 0, 0 ]	1	560
25	[ 0, 0, 0, 0, 0, 1, 0 ]	4	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	13	1

Highest weight: [ 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: not 3,5
Dimension: 910

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 0, 0, 1, 0, 0, 0 ]	1	560
25	[ 0, 0, 0, 0, 0, 1, 0 ]	4	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	14	1

Highest weight: [ 0, 1, 0, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 1093

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 1, 0, 0, 0, 0, 0 ]	1	448
41	[ 0, 0, 0, 1, 0, 0, 0 ]	1	560
25	[ 0, 0, 0, 0, 0, 1, 0 ]	1	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	1	1

Highest weight: [ 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 1094

Level	dominant weight	weight multiplicity	length of W-orbit
50	[ 1, 0, 0, 0, 0, 0, 0 ]	1	128
46	[ 0, 0, 1, 0, 0, 0, 0 ]	1	672
34	[ 0, 0, 0, 0, 1, 0, 0 ]	1	280
14	[ 0, 0, 0, 0, 0, 0, 1 ]	1	14

Highest weight: [ 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 1288

Level	dominant weight	weight multiplicity	length of W-orbit
46	[ 0, 0, 1, 0, 0, 0, 0 ]	1	672
34	[ 0, 0, 0, 0, 1, 0, 0 ]	2	280
14	[ 0, 0, 0, 0, 0, 0, 1 ]	4	14

Highest weight: [ 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: not 2,3
Dimension: 1430

Level	dominant weight	weight multiplicity	length of W-orbit
50	[ 1, 0, 0, 0, 0, 0, 0 ]	1	128
46	[ 0, 0, 1, 0, 0, 0, 0 ]	1	672
34	[ 0, 0, 0, 0, 1, 0, 0 ]	2	280
14	[ 0, 0, 0, 0, 0, 0, 1 ]	5	14

Highest weight: [ 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 5
Dimension: 1624

Level	dominant weight	weight multiplicity	length of W-orbit
46	[ 0, 0, 1, 0, 0, 0, 0 ]	1	672
34	[ 0, 0, 0, 0, 1, 0, 0 ]	3	280
14	[ 0, 0, 0, 0, 0, 0, 1 ]	8	14

Highest weight: [ 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: not 2,5
Dimension: 1638

Level	dominant weight	weight multiplicity	length of W-orbit
46	[ 0, 0, 1, 0, 0, 0, 0 ]	1	672
34	[ 0, 0, 0, 0, 1, 0, 0 ]	3	280
14	[ 0, 0, 0, 0, 0, 0, 1 ]	9	14

Highest weight: [ 1, 0, 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 1792

Level	dominant weight	weight multiplicity	length of W-orbit
63	[ 1, 0, 0, 0, 0, 0, 1 ]	1	896
49	[ 0, 1, 0, 0, 0, 0, 0 ]	2	448

Highest weight: [ 0, 1, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 1912

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 1, 0, 0, 0, 0, 0 ]	1	448
41	[ 0, 0, 0, 1, 0, 0, 0 ]	2	560
25	[ 0, 0, 0, 0, 0, 1, 0 ]	4	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	8	1

Highest weight: [ 0, 1, 0, 0, 0, 0, 0 ]
Characteristic: 5
Dimension: 2001

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 1, 0, 0, 0, 0, 0 ]	1	448
41	[ 0, 0, 0, 1, 0, 0, 0 ]	2	560
25	[ 0, 0, 0, 0, 0, 1, 0 ]	5	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	13	1

Highest weight: [ 0, 1, 0, 0, 0, 0, 0 ]
Characteristic: not 2,3,5
Dimension: 2002

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 1, 0, 0, 0, 0, 0 ]	1	448
41	[ 0, 0, 0, 1, 0, 0, 0 ]	2	560
25	[ 0, 0, 0, 0, 0, 1, 0 ]	5	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	14	1

Highest weight: [ 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 2184

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 0, 0, 2, 0 ]	1	84
47	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
41	[ 0, 0, 0, 1, 0, 0, 0 ]	1	560
27	[ 0, 0, 0, 0, 0, 0, 2 ]	6	14
25	[ 0, 0, 0, 0, 0, 1, 0 ]	7	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	28	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3
Dimension: 2380

Level	dominant weight	weight multiplicity	length of W-orbit
53	[ 0, 0, 0, 0, 0, 0, 4 ]	1	14
51	[ 0, 0, 0, 0, 0, 1, 2 ]	1	168
49	[ 0, 0, 0, 0, 0, 2, 0 ]	1	84
47	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
41	[ 0, 0, 0, 1, 0, 0, 0 ]	1	560
27	[ 0, 0, 0, 0, 0, 0, 2 ]	7	14
25	[ 0, 0, 0, 0, 0, 1, 0 ]	7	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	28	1

Highest weight: [ 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 2884

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
41	[ 0, 0, 0, 1, 0, 0, 0 ]	2	560
27	[ 0, 0, 0, 0, 0, 0, 2 ]	4	14
25	[ 0, 0, 0, 0, 0, 1, 0 ]	10	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	28	1

Highest weight: [ 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 5
Dimension: 3093

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 0, 0, 2, 0 ]	1	84
47	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
41	[ 0, 0, 0, 1, 0, 0, 0 ]	2	560
27	[ 0, 0, 0, 0, 0, 0, 2 ]	6	14
25	[ 0, 0, 0, 0, 0, 1, 0 ]	11	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	41	1

Highest weight: [ 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,5
Dimension: 3094

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 0, 0, 2, 0 ]	1	84
47	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
41	[ 0, 0, 0, 1, 0, 0, 0 ]	2	560
27	[ 0, 0, 0, 0, 0, 0, 2 ]	6	14
25	[ 0, 0, 0, 0, 0, 1, 0 ]	11	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	42	1

Highest weight: [ 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: 3
Dimension: 3795

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
41	[ 0, 0, 0, 1, 0, 0, 0 ]	3	560
27	[ 0, 0, 0, 0, 0, 0, 2 ]	4	14
25	[ 0, 0, 0, 0, 0, 1, 0 ]	14	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	43	1

Highest weight: [ 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: 7
Dimension: 3811

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
41	[ 0, 0, 0, 1, 0, 0, 0 ]	3	560
27	[ 0, 0, 0, 0, 0, 0, 2 ]	5	14
25	[ 0, 0, 0, 0, 0, 1, 0 ]	14	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	45	1

Highest weight: [ 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: not 2,3,7
Dimension: 3900

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
41	[ 0, 0, 0, 1, 0, 0, 0 ]	3	560
27	[ 0, 0, 0, 0, 0, 0, 2 ]	5	14
25	[ 0, 0, 0, 0, 0, 1, 0 ]	15	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	50	1

Highest weight: [ 0, 0, 0, 0, 0, 1, 2 ]
Characteristic: not 2
Dimension: 5355

Level	dominant weight	weight multiplicity	length of W-orbit
51	[ 0, 0, 0, 0, 0, 1, 2 ]	1	168
49	[ 0, 0, 0, 0, 0, 2, 0 ]	1	84
47	[ 0, 0, 0, 0, 1, 0, 1 ]	2	840
41	[ 0, 0, 0, 1, 0, 0, 0 ]	3	560
27	[ 0, 0, 0, 0, 0, 0, 2 ]	12	14
25	[ 0, 0, 0, 0, 0, 1, 0 ]	18	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	63	1