A029897 Theta series of 13-dimensional lattice Kappa_13 with minimal norm 4.

1, 0, 918, 6624, 36450, 120096, 322436, 764640, 1637766, 2912544, 5591592, 9160992, 14668002, 22913280, 35544420, 48529440, 74114514, 100230912, 136486530, 184801824, 252809100, 308852640, 426995388, 528491520, 664053284, 836215488, 1070501400, 1229873472

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			G.f. = 1 + 918*q^4 + 6624*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..1000
• G. Nebe and N. J. A. Sloane, Home page for this lattice

Programs

Magma

L := (Lattice("Kappa", 13));
B := Basis(ThetaSeriesModularFormSpace(L), 55);
S := [1, 0, 918, 6624, 36450, 120096, 322436, 764640, 1637766, 2912544, 5591592, 9160992, 14668002, 22913280, 35544420, 48529440, 74114514, 100230912, 136486530, 184801824, 252809100, 308852640, 426995388, 528491520, 664053284];
Coefficients(&+[B[i] * S[i] : i in [1..25]]); // Andy Huchala, Jul 23 2021

Extensions

More terms from Andy Huchala, Jul 23 2021