A362879 Theta series of 19-dimensional lattice Kappa_19.

1, 0, 9396, 284528, 3309660, 21996036, 103632480, 384538752, 1195104618, 3253783500, 7971340896, 17905302720, 37530681590, 74139276672, 139067432280, 250102136592, 433070833500, 724358442744, 1178016364548, 1866143480400, 2883345017508, 4367172766500

Offset

0,3

Comments

Theta series is an element of the space of modular forms on Gamma_0(12) of weight 19/2 and dimension 19 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 + 9396*q^4 + 284528*q^6 + ...

Prog

(Magma)
prec := 30;
coeffs := [1, 0, 9396, 284528, 3309660, 21996036, 103632480, 384538752, 1195104618, 3253783500, 7971340896, 17905302720, 37530681590, 74139276672, 139067432280, 250102136592, 433070833500, 724358442744, 1178016364548];
ls := [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, 0, 0, 0, 0, 0, 0, -2, 4, 0, -1, 0, 0, 1, 1, 0, 1, 1, -1, 0, 0, 1, -1, 4, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 1, 4, 1, 0, -1, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 4];
S := SymmetricMatrix(ls);
L := LatticeWithGram(S);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
Coefficients(&+[coeffs[i]*B[i] :i in [1..19]]);

Crossrefs

Cf. A029897, A047628, A362875, A362876, A362877, A362878, A362880.

Sequence in context: A045202 A202645 A183796 * A183733 A290424 A210082

Adjacent sequences: A362876 A362877 A362878 * A362880 A362881 A362882

Keyword

nonn

Author

Andy Huchala, May 08 2023

Status

approved