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%I M5467 #23 May 13 2023 01:58:22
%S 1,0,632,3328,18440,44032,139872,236032,589576,829440,1803600,2250496,
%T 4499360,5196800,9676480,10694144,18865928,19884032,34147224,34636032,
%U 57643440,57413632,92796192,90131968,143856544,136744960,213841936,201703936,309939520
%N Theta series of laminated lattice LAMBDA_12^{mid}.
%C Theta series is an element of the space of modular forms on Gamma_0(8) of weight 6 and dimension 7 over the integers. - _Andy Huchala_, May 10 2023
%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="/A006913/b006913.txt">Table of n, a(n) for n = 0..20000</a>
%H G. Nebe and N. J. A. Sloane, <a href="https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA12_MID.html">Home page for this lattice</a>
%o (Magma)
%o prec := 20;
%o S := SymmetricMatrix([4,2,4,0,-2,4,0,-2,0,4,0,0,-2,0,4,-2,-2,0,0,0,4,0,0,0,0,0,-2,4,0,0,0,0,0,0,-2,4,0,0,0,0,1,-1,0,0,4,0,0,0,0,-1,0,0,0,0,4,0,0,0,0,0,0,0,0,-2,0,4,0,1,-2,0,1,0,0,-1,1,0,0,4]);
%o L := LatticeWithGram(S);
%o T<q> := ThetaSeries(L, 12);
%o M := ThetaSeriesModularFormSpace(L);
%o B := Basis(M,prec);
%o Coefficients(&+[Coefficients(T)[2*i-1]*B[i] : i in [1..7]]); // _Andy Huchala_, May 10 2023
%K nonn,nice,easy
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _Andy Huchala_, May 10 2023
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