login
Theta series of D*_16 lattice.
1

%I #14 Jul 14 2021 02:16:26

%S 1,32,480,4480,94688,140736,1574528,1580800,11858400,8945824,56374848,

%T 36714624,202983040,118156480,593481984,321692928,1519972832,

%U 772845120,3450308960,1681379200,7246599744,3392205824,14048841600,6411152640,25979733632,11488092896

%N Theta series of D*_16 lattice.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.

%H Andy Huchala, <a href="/A022069/b022069.txt">Table of n, a(n) for n = 0..20000</a>

%e G.f. = 1 + 32*q^2 + 480*q^4 + ...

%o (Sage)

%o L = [1, 32, 480]

%o M = ModularForms(Gamma0(2),8)

%o bases = [_.q_expansion(30) for _ in M.integral_basis()]

%o f = sum(x*y for (x,y) in zip(bases,L)); list(f) # _Andy Huchala_, Jul 13 2021

%K nonn

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Andy Huchala_, Jul 13 2021