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 13:27:33 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
GRAM
PROPERTIES
REMARKS
LAST_LINE

• NAME
  dim16mod7
  

• DIMENSION
  16
  

• DIVISORS
  1 1 1 1 1 1 1 1 7 7 7 7 7 7 7 7
  

• MINIMAL_NORM
  6
  

• KISSING_NUMBER
  480
  

• GROUP_ORDER
  2^7 * 3^2 * 5^2
  

• GROUP_NAME
  SL2(5) o SL2(5) : 2
  

• GROUP_GENERATORS
  3
  16 16
  0 0 0 0 0 0 0 0 1 0 0 0 -1 0 1 0
  0 0 0 0 0 0 0 0 0 -1 -1 0 0 1 -1 0
  0 0 0 0 0 0 0 0 0 -1 -1 0 -1 0 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 -1 1 1 0 -1
  0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0
  0 0 0 0 0 0 0 0 -1 0 0 0 -1 -1 0 1
  -1 -1 1 1 -1 1 1 -1 0 0 0 0 0 0 0 0
  -1 -1 1 1 -1 1 0 -1 0 0 0 0 0 0 0 0
  1 0 -1 -1 1 -1 0 1 0 0 0 0 0 0 0 0
  1 1 0 -1 0 0 -1 1 0 0 0 0 0 0 0 0
  -1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0
  0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 -1 1 1 -1 1 1 -1 0 0 0 0 0 0 0 0
  16 16
  0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0
  1 1 -1 0 0 0 -1 1 0 0 0 0 0 0 0 0
  -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
  -1 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0
  1 0 -1 0 1 0 0 1 0 0 0 0 0 0 0 0
  2 1 0 -1 0 0 -1 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 -1 -1 -1 -2 0 0 -1 0
  0 0 0 0 0 0 0 0 -1 0 0 -1 1 0 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
  0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 1 1
  0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 -1
  0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0
  0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0
  16 16
  0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0
  0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 -1 0 1 0 0 1 0 0 0 0 0 0 0 0
  1 0 0 -1 1 0 0 1 0 0 0 0 0 0 0 0
  1 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0
  0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0
  0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1
  0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0
  
  

• GRAM
  16 16
  6 -2 1 3 -2 0 3 -1 2 0 0 0 0 0 0 0
  -2 6 3 1 2 -1 1 0 0 2 0 0 0 0 0 0
  1 3 6 3 0 -3 3 2 0 0 2 0 0 0 0 0
  3 1 3 6 -2 -3 3 2 0 0 0 2 0 0 0 0
  -2 2 0 -2 6 3 -3 -3 0 0 0 0 2 0 0 0
  0 -1 -3 -3 3 6 -3 -3 0 0 0 0 0 2 0 0
  3 1 3 3 -3 -3 6 2 0 0 0 0 0 0 2 0
  -1 0 2 2 -3 -3 2 6 0 0 0 0 0 0 0 2
  2 0 0 0 0 0 0 0 12 6 -4 -6 3 -5 -5 6
  0 2 0 0 0 0 0 0 6 6 -3 -3 0 -2 -3 3
  0 0 2 0 0 0 0 0 -4 -3 6 1 -3 3 0 -3
  0 0 0 2 0 0 0 0 -6 -3 1 6 -1 3 2 -3
  0 0 0 0 2 0 0 0 3 0 -3 -1 6 -3 1 3
  0 0 0 0 0 2 0 0 -5 -2 3 3 -3 6 2 -2
  0 0 0 0 0 0 2 0 -5 -3 0 2 1 2 6 -2
  0 0 0 0 0 0 0 2 6 3 -3 -3 3 -2 -2 6
  
  

• PROPERTIES
  INTEGRAL =1
  MODULAR = 7
  

• REMARKS
  Found by Gabriele Nebe using the convenient construction described in Bachoc/Nebe (Crelle 1998)
  If F is the GramMatrix of the extremal 11-modular lattice with
  automorphism group SL2(5)oSL2(5) of dimension 8
  then the GramMatrix of this lattice is the block matrix
  F 2I8
  2I8 11F^-1
  Its automorphism group is diag(g,g^{-tr}) (the obvious subgroup) with g in Aut(F)
  extended by the isometry between F and 11 F^-1.
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe