A029696 Theta series of 7-dimensional lattice Kappa_7*.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 22, 0, 0, 64, 0, 0, 0, 0, 40, 0, 0, 64, 44, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 240, 0, 0, 448, 0, 0, 0, 0, 112, 0, 0, 384, 480, 0, 0, 0, 0, 0, 0, 0, 220, 0, 0, 0, 450, 0, 0, 1408, 0, 0, 0, 0, 480, 0, 0, 960, 812

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			G.f. = 1 + 2*q^12 + 22*q^16 + ...
		

References

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

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..1000
• Sean A. Irvine, Java program (github)
• G. Nebe and N. J. A. Sloane, Home page for this lattice

Crossrefs

Cf. A015236.

Programs

Magma

L := Dual(Lattice("Kappa", 7));
B := Basis(ThetaSeriesModularFormSpace(L), 100);
S := [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 22, 0, 0, 64, 0, 0, 0, 0, 40, 64];
Coefficients(&+[B[i] * S[i] : i in [1..26]]); // Andy Huchala, Jul 24 2021

Extensions

More terms from Sean A. Irvine, Mar 02 2020