A362876 Theta series of 16-dimensional lattice Kappa_16.

1, 0, 2772, 42624, 335052, 1545984, 5698860, 16297344, 42785244, 94440960, 204094296, 385391232, 730053060, 1240934400, 2151268128, 3374469504, 5476016700, 8115545088, 12477938100, 17677480320, 26111897640, 35570481408, 50909418000, 67336722432, 93433877268

Offset

0,3

Comments

Theta series is an element of the space of modular forms on Gamma_0(12) of weight 8 and dimension 17 over the integers.

References

J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Chap. 6.

Links

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

G. Nebe and N. J. A. Sloane, Home page for this lattice.

Example

G.f. = 1 + 2772*q^4 + 42624*q^6 + ...

Prog

(Magma)
prec := 40;
S := SymmetricMatrix([4, 2, 4, 0, -2, 4, 0, -2, 0, 4, 0, 0, -2, 0, 4, -2, -2, 0, 0, 0, 4, -2, -1, 1, 0, 0, 0, 4, -2, -1, 0, -1, 1, 2, 2, 4, -2, -2, 0, 1, 1, 2, 2, 2, 4, -2, 0, -2, 0, 1, 1, 0, 0, 0, 4, 1, 1, 0, 0, 0, -2, 0, -1, -1, -2, 4, -2, -1, 0, 0, 0, 1, 1, 1, 1, 1, -2, 4, 0, -1, 1, 1, 0, -1, 1, 0, 0, -1, 1, -1, 4, 0, 0, 0, 0, 0, 0, 1, 0, 1, -1, 1, -1, 1, 4, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 0, 0, -1, 4, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, -1, 4]);
L := LatticeWithGram(S);
T<q> := ThetaSeries(L, 32);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
Coefficients(&+[Coefficients(T)[2*i-1]*B[i] : i in [1..17]]);

Crossrefs

Cf. A029897, A047628, A362875, A362877, A362878, A362879, A362880.

Sequence in context: A249228 A154081 A387457 * A099691 A231739 A251200

Adjacent sequences: A362873 A362874 A362875 * A362877 A362878 A362879

Keyword

nonn

Author

Andy Huchala, May 07 2023

Status

approved