A362877 Theta series of 17-dimensional lattice Kappa_17.

1, 0, 4266, 81792, 737862, 3809280, 15406210, 47505792, 133390290, 312588288, 711232812, 1408787328, 2789963820, 4931371008, 8870944884, 14417119872, 24144502662, 36878456832, 58393537998, 84926534016

Offset

0,3

Comments

Theta series is an element of the space of modular forms on Gamma_1(48) with Kronecker character 12 in modulus 48, weight 17/2, and dimension 66 over the integers.

References

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

Links

Table of n, a(n) for n=0..19.

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

Example

G.f. = 1 + 4266*q^4 + 81792*q^6 + ...

Prog

(Magma)
prec := 10;
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, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 1, -1, 1, 0, 1, -1, 4]);
L := LatticeWithGram(S);
T<q> := ThetaSeries(L, 2*prec);
[Coefficients(T)[2*i-1] : i in [1..prec]];

Crossrefs

Cf. A029897, A047628, A362875, A362876, A362878, A362879, A362880.

Sequence in context: A023346 A231195 A342565 * A237459 A259951 A101619

Adjacent sequences: A362874 A362875 A362876 * A362878 A362879 A362880

Keyword

nonn

Author

Andy Huchala, May 07 2023

Status

approved