login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A345662 Theta series of the canonical laminated lattice LAMBDA_31. 0
1, 0, 0, 0, 202692, 516096, 29046528, 145195008, 1538419918, 6537101312, 36946043904, 124680077312, 511130138792, 1419643330560, 4752698632192 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Theta series is an element of the space of modular forms on Gamma_1(32) with Kronecker character 8 in modulus 32, weight 31/2, and dimension 62 over the integers.
As of version 2.26-4, the largest rank of a laminated lattice which is recognized by Magma is 31, but laminated lattices of larger rank exist (see Conway and Sloane reference).
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 179.
LINKS
J. H. Conway and N. J. A. Sloane, Laminated lattices, Annals of Math., 116 (1982), pp. 593-620. A revised version appears as Chapter 6 of "Sphere Packings, Lattices and Groups" by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.
J. H. Conway and N. J. A. Sloane, The "shower" showing containments among the laminated lattices up to dimension 48 (Fig 3 from the Annals paper, also Fig. 6.1 in the Sphere packing book).
G. Nebe and N. J. A. Sloane, Home page for this lattice
EXAMPLE
G.f.: 1 + 202692*q^8 + 516096*q^10 + ...
PROG
(Magma)
L := Lattice("Lambda", 31);
T<q> := ThetaSeries(L, 14);
C := Coefficients(T);
[C[2*i-1] : i in [1..8]];
CROSSREFS
Sequence in context: A235929 A172623 A172728 * A290505 A205891 A186532
KEYWORD
nonn,more
AUTHOR
Andy Huchala, Jun 29 2021
EXTENSIONS
a(11)-a(14) from Robin Visser, Sep 24 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 13 12:08 EDT 2024. Contains 371641 sequences. (Running on oeis4.)