A015235 Theta series of lattice Kappa_8.

1, 0, 132, 192, 828, 1152, 2796, 2880, 6828, 5376, 14904, 10944, 20772, 18432, 40224, 25920, 53964, 41472, 76452, 58176, 107784, 69504, 156816, 101376, 163284, 131328, 259032, 147072, 295200, 206208, 357480, 250560, 432780, 269568, 576072, 365184, 555804, 426240

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			G.f. = 1 + 132*q^4 + 192*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..20000
• G. Nebe and N. J. A. Sloane, Home page for this lattice

Crossrefs

Cf. A015236 (K_7), A015233 (K_9), A015232 (K_10), A015229 (K_11), A004010 (K_12), A029897 (K_13), A047628 (K_14).

Programs

Sage

L = [1, 0, 132, 192, 828, 1152, 2796, 2880, 6828, 5376]
M = ModularForms(Gamma0(12),4)
bases = [.q_expansion(35) for  in M.integral_basis()]
f = sum(x*y for (x,y) in zip(bases,L)); list(f) # Andy Huchala, Jul 23 2021

Extensions

More terms from Sean A. Irvine, Feb 26 2020