The Lattice DualExtremal(4,11)
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwth-aachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:27:53 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME (required)
DIMENSION (required)
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
THETA_SERIES
PROPERTIES
REFERENCES
NOTES
URL (links to other sites for this lattice)
LAST_LINE (required)
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NAME (required)
DualExtremal(4,11)
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DIMENSION (required)
4
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GRAM (floating point or integer Gram matrix)
4
4 1 1 -2
1 4 2 -1
1 2 4 0
-2 -1 0 4
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DIVISORS (elementary divisors)
11^2
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MINIMAL_NORM
4
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THETA_SERIES
1 + 12*q^4 + 12*q^6 + 12*q^8 + 12*q^10 + 24*q^12 + 24*q^14 + 36*q^16 + 36*q^18
+ 48*q^20 + 72*q^24 + 24*q^26 + 48*q^28 + 60*q^30 + 84*q^32 + 48*q^34 +
84*q^36 + 48*q^38 + 96*q^40 + 72*q^42 + 12*q^44 + 60*q^46 + 144*q^48 +
84*q^50 + 120*q^52 + 84*q^54 + 144*q^56 + 72*q^58 + 168*q^60 + 60*q^62 +
132*q^64 + 12*q^66 + 120*q^68 + 120*q^70 + 228*q^72 + 84*q^74 + 144*q^76 +
144*q^78 + 216*q^80 + 120*q^82 + 240*q^84 + 120*q^86 + 12*q^88 + 192*q^90 +
168*q^92 + 96*q^94 + 288*q^96 + 144*q^98 + 204*q^100 + 168*q^102 +
216*q^104 + 144*q^106 + 312*q^108 + 12*q^110 + 288*q^112 + 192*q^114 +
216*q^116 + 132*q^118 + 408*q^120 + 120*q^122 + 264*q^124 + 240*q^126 +
324*q^128 + 192*q^130 + 24*q^132 + 180*q^134 + 312*q^136 + 228*q^138 +
336*q^140 + 180*q^142 + 468*q^144 + 168*q^146 + 288*q^148 + 288*q^150 +
336*q^152 + 24*q^154 + 384*q^156 + 216*q^158 + 456*q^160 + 288*q^162 +
264*q^164 + 216*q^166 + 528*q^168 + 264*q^170 + 288*q^172 + 288*q^174 +
36*q^176 + 180*q^178 + 552*q^180 + 288*q^182 + 408*q^184 + 324*q^186 +
384*q^188 + 288*q^190 + 624*q^192 + 252*q^194 + 396*q^196 + 36*q^198 +
540*q^200 +
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PROPERTIES
INTEGRAL = 1 (lattices are real unless stated otherwise)
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REFERENCES
Boecherer, Nebe: On theta series attached to maximal lattices and their adjoints.
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NOTES
The dual of a maximal integral lattice of level 11
with highest possible minimum.
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URL (links to other sites for this lattice)
-
LAST_LINE (required)
Haftungsausschluss/Disclaimer
Gabriele Nebe