A047627 Theta series of 14-dimensional integral laminated lattice LAMBDA14.4 with minimal norm 4.

1, 0, 1210, 11552, 71192, 254656, 804528, 1915328, 4538956, 8628864, 17309892, 28803296, 51649344, 78486464, 130311456, 185010752, 290432044, 392591488, 587974442, 765028512, 1108040944, 1392702208, 1962884944, 2407505728, 3303637472, 3970663680, 5347655844

Offset

0,3

Comments

This theta series is an element of the space of modular forms on Gamma_1(32) with Kronecker character -4 in modulus 32, weight 7, and dimension 28. - Andy Huchala, May 15 2023

Links

Andy Huchala, Table of n, a(n) for n = 0..10000

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

Prog

(Magma)
prec := 30;
gram := [4, 2, 4, 0, -2, 4, 0, -2, 0, 4, 0, 0, -2, 0, 4, -2, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 1, -1, 0, 0, 4, 0, 0, 0, 0, -1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 1, -2, 0, 1, 0, 0, -1, 1, 0, 0, 4, -1, 0, -1, -1, 1, 0, 1, 0, 1, 1, 0, 0, 4, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 1, 1, 4];
S := SymmetricMatrix(gram);
L := LatticeWithGram(S);
T := ThetaSeriesModularForm(L);
Coefficients(PowerSeries(T, prec)); // Andy Huchala, May 15 2023

Crossrefs

Cf. A023937, A046958, A047626.

Sequence in context: A359049 A358711 A138480 * A252213 A258727 A234544

Adjacent sequences: A047624 A047625 A047626 * A047628 A047629 A047630

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Andy Huchala, May 15 2023

Status

approved