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%I M5439 #24 Jun 14 2021 15:57:47
%S 1,0,336,768,4950,6912,22944,27648,75792,72192,181728,158976,393030,
%T 317952,682656,557568,1249686,912384,1881840,1458432,2979072,2155776,
%U 4254048,3055104,6251808,4354560
%N Theta series of laminated lattice LAMBDA_10.
%C This is the q-expansion corresponding to the vector [1, 0, 336, 768, 4950, 6912, 22944, 27648, 75792, 72192, 181728, 158976] in the space of modular forms on Gamma_1(12) with character Kronecker character -3 in modulus 12, weight 5, and dimension 11 over Integer Ring in the basis ordered by degree of leading term (as in Magma).
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 157.
%D E. C. Pervin, personal communication.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andy Huchala, <a href="/A006909/b006909.txt">Table of n, a(n) for n = 0..20000</a>
%e G.f.: 1 + 336*q^4 + 768*q^6 + 4950*q^8 + ...
%o (Sage)
%o e = DirichletGroup(12).1
%o M = ModularForms(e, 5, QQ)
%o bases = [_.q_expansion(20) for _ in M.integral_basis()]
%o list(sum(x*y for (x,y) in zip(bases,[1, 0, 336, 768, 4950, 6912, 22944, 27648, 75792, 72192, 181728, 158976]))) # _Andy Huchala_, Jun 05 2021
%K nonn
%O 0,3
%A _N. J. A. Sloane_
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