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%I #19 Jun 25 2021 23:39:47
%S 1,0,0,0,197736,98304,19104768,27131904,604372968,1099235328,
%T 9814781952,17547657216,100353367584,162948022272,731010140160,
%U 1065852469248,4124381085672,5447639433216,19044567785472,23134041538560,74959792721136,84922989674496
%N Theta series of the canonical laminated lattice LAMBDA_28.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag. See pp. 159, 179.
%H Andy Huchala, <a href="/A345659/b345659.txt">Table of n, a(n) for n = 0..20000</a>
%H J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.2307/2007025">Laminated lattices</a>, Annals of Math., 116 (1982), pp. 593-620. A revised version appears as Chapter 6 of "Sphere Packings, Lattices and Groups" by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.
%H J. H. Conway and N. J. A. Sloane, <a href="/A005135/a005135.png">The "shower" showing containments among the laminated lattices up to dimension 48</a> (Fig 3 from the Annals paper, also Fig. 6.1 in the Sphere packing book).
%H G. Nebe and N. J. A. Sloane, <a href="https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA28.html">Home page for this lattice</a>
%H <a href="/index/La#laminated">Index entries for sequences related to laminated lattices</a>
%e G.f.: 1 + 197736*q^8 + 98304*q^10 + ...
%o (Sage)
%o L = [1, 0, 0, 0, 197736, 98304, 19104768, 27131904, 604372968, 1099235328, 9814781952, 17547657216, 100353367584, 162948022272, 731010140160]
%o M = ModularForms(Gamma0(8),14)
%o bases = [_.q_expansion(100) for _ in M.integral_basis()]
%o f = sum(x*y for (x,y) in zip(bases,L)); list(f)
%K nonn
%O 0,5
%A _Andy Huchala_, Jun 21 2021
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