A345659 Theta series of the canonical laminated lattice LAMBDA_28.

1, 0, 0, 0, 197736, 98304, 19104768, 27131904, 604372968, 1099235328, 9814781952, 17547657216, 100353367584, 162948022272, 731010140160, 1065852469248, 4124381085672, 5447639433216, 19044567785472, 23134041538560, 74959792721136, 84922989674496

Offset

0,5

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag. See pp. 159, 179.

Links

Andy Huchala, Table of n, a(n) for n = 0..20000

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 + 197736*q^8 + 98304*q^10 + ...

Prog

(Sage)
L = [1, 0, 0, 0, 197736, 98304, 19104768, 27131904, 604372968, 1099235328, 9814781952, 17547657216, 100353367584, 162948022272, 731010140160]
M = ModularForms(Gamma0(8), 14)
bases = [_.q_expansion(100) for _ in M.integral_basis()]
f = sum(x*y for (x, y) in zip(bases, L)); list(f)

Crossrefs

Sequence in context: A099818 A345658 A185519 * A344942 A344943 A213817

Adjacent sequences: A345656 A345657 A345658 * A345660 A345661 A345662

Keyword

nonn

Author

Andy Huchala, Jun 21 2021

Status

approved