A015233 Theta series of lattice Kappa_9.

1, 0, 180, 416, 1620, 3024, 6404, 9408, 18876, 20048, 43224, 45408, 70462, 82272, 138408, 121600, 213972, 210816, 298620, 310176, 472464, 391376, 675168, 604032, 794524, 808512, 1208568, 949568, 1533048, 1361328, 1781632, 1719744, 2435580, 1916336, 3092616

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			G.f. = 1 + 180*q^4 + 416*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..1500
• G. Nebe and N. J. A. Sloane, Home page for this lattice

Programs

Magma

L := (Lattice("Kappa", 9));
B := Basis(ThetaSeriesModularFormSpace(L), 100);
S := [1, 0, 180, 416, 1620, 3024, 6404, 9408, 18876, 20048, 43224, 45408, 70462, 82272, 138408, 121600, 213972, 210816, 298620, 310176, 472464, 391376, 675168, 604032, 794524, 808512, 1208568, 949568, 1533048, 1361328, 1781632, 1719744, 2435580, 1916336];
Coefficients(&+[B[i] * S[i] : i in [1..34]]); // Andy Huchala, Jul 23 2021

Extensions

a(16)-a(25) from Sean A. Irvine, Feb 28 2020

More terms from Andy Huchala, Jul 23 2021