A047628 Theta series of 14-dimensional lattice Kappa_{14} with minimal norm 4.

1, 0, 1242, 11916, 72252, 266544, 807090, 2006856, 4603284, 8924940, 17571816, 30168396, 51799212, 82147608, 132245676, 191541024, 294596676, 410924988, 590219898, 800792568, 1123700904, 1442103768, 1991926080, 2519984088, 3314316426, 4155999192, 5427108108

Offset

0,3

Comments

Theta series is an element of the space of modular forms on Gamma_1(18) with Kronecker character -3 in modulus 18, weight 7, and dimension 22 over the integers. - Andy Huchala, May 07 2023

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

Prog

(Magma)
prec := 80;
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]);
L := LatticeWithGram(S);
T<q> := ThetaSeries(L, 42);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
Coefficients(&+[Coefficients(T)[2*i-1]*B[i] :i in [1..22]]); // Andy Huchala, May 07 2023

Crossrefs

Cf. A029897, A362875, A362876, A362877, A362878, A362879, A362880.

Sequence in context: A099178 A209711 A228964 * A181073 A023065 A190413

Adjacent sequences: A047625 A047626 A047627 * A047629 A047630 A047631

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Andy Huchala, May 07 2023

Status

approved