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 13:27:51 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)

• NAME (required)
  DualExtremal(4,5)
  

• DIMENSION (required)
  4
  

• GRAM (floating point or integer Gram matrix)
  4
  2 1 -1 1
  1 2 -1 0
  -1 -1 4 -2
  1 0 -2 4
  

• DIVISORS (elementary divisors)
  5^2
  

• MINIMAL_NORM
  2
  

• THETA_SERIES
  1 + 6*q^2 + 18*q^4 + 24*q^6 + 42*q^8 + 6*q^10 + 72*q^12 + 48*q^14 + 90*q^16 +
  78*q^18 + 18*q^20
  

• PROPERTIES
  INTEGRAL = 1 (lattices are real unless stated otherwise)
  

• REFERENCES
  Boecherer, Nebe: On theta series attached to maximal lattices and their adjoints.
  

• NOTES
  The dual of a maximal integral lattice of level 5
  with highest possible minimum.
  Here it is just the norm form of the definite quaternion algebra
  ramified only at 5.
  

• URL (links to other sites for this lattice)
  

• LAST_LINE (required)
  
  
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe