A345661 Theta series of the canonical laminated lattice LAMBDA_30.

1, 0, 0, 0, 200046, 294912, 23779584, 82378752, 1032132696, 3570794496, 21539288064, 64122912768, 266965225878, 683889819648, 2273486860032, 5134106886144

Offset

0,5

Comments

Theta series is an element of the space of modular forms on Gamma_1(24) with Kronecker character -3 in modulus 24, weight 15, and dimension 60 over the integers.

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..15.

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

1 + 200046*q^8 + 294912*q^10 + ...

Prog

(Magma)
L := Lattice("Lambda", 30);
T<q> := ThetaSeries(L, 14);
C := Coefficients(T);
[C[2*i-1] : i in [1..8]];

Crossrefs

Cf. A005135, A023942, A008408.

Sequence in context: A200863 A345637 A346350 * A363167 A179224 A237374

Adjacent sequences: A345658 A345659 A345660 * A345662 A345663 A345664

Keyword

nonn,more

Author

Andy Huchala, Jun 29 2021

Extensions

a(11)-a(15) from Robin Visser, Sep 24 2023

Status

approved