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

Author

Andy Huchala, Jun 29 2021

Keywords

• nonn
• more

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).

Examples

			G.f.: 1 + 202692*q^8 + 516096*q^10 + ...
		

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
• Index entries for sequences related to laminated lattices

Crossrefs

Cf. A005135, A023942, A008408, A002336.

Programs

Magma

L := Lattice("Lambda", 31);
T := ThetaSeries(L,14);
C := Coefficients(T);
[C[2*i-1] : i in [1..8]];

Extensions

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