A015236 Theta series of lattice Kappa_7.

1, 0, 92, 64, 436, 320, 1248, 640, 2476, 1024, 5080, 1984, 6170, 2944, 11704, 3840, 13860, 6144, 19964, 7744, 24064, 8768, 36944, 12800, 33888, 15360, 54808, 16768, 57176, 22464, 71416, 25984, 79628, 27648, 107128, 35840, 93844, 41984, 143888, 42112, 137720

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			G.f. = 1 + 92*q^4 + 64*q^6 + ...
		

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 161.

Links

• Andy Huchala, Table of n, a(n) for n = 0..1880
• G. Nebe and N. J. A. Sloane, Home page for this lattice

Programs

Magma

L := (Lattice("Kappa", 7));
B := Basis(ThetaSeriesModularFormSpace(L), 30);
S := [1, 0, 92, 64, 436, 320, 1248, 640, 2476, 1024, 5080, 1984, 6170, 2944, 11704, 3840, 13860, 6144, 19964, 7744, 24064, 8768, 36944, 12800, 33888, 15360];
Coefficients(&+[B[i] * S[i] : i in [1..26]]); // Andy Huchala, Jul 18 2021

Extensions

More terms from Sean A. Irvine, Feb 25 2020