A345662 Theta series of the canonical laminated lattice LAMBDA_31.

1, 0, 0, 0, 202692, 516096, 29046528, 145195008, 1538419918, 6537101312, 36946043904, 124680077312, 511130138792, 1419643330560, 4752698632192

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

Table of n, a(n) for n=0..14.

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

Index entries for sequences related to laminated lattices

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

Cf. A005135, A023942, A008408, A002336.

Sequence in context: A235929 A172623 A172728 * A290505 A205891 A186532

Adjacent sequences: A345659 A345660 A345661 * A345663 A345664 A345665

Keyword

nonn,more

Author

Andy Huchala, Jun 29 2021

Extensions

a(11)-a(14) from Robin Visser, Sep 24 2023

Status

approved