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%I M5484 #24 May 08 2023 09:36:20
%S 1,0,890,6400,36600,110080,337520,698880,1649610,2780160,5619792,
%T 8387840,15347280,20974080,35834560,46174720,74480280,92062720,
%U 142597450,169132800,254916880,293647360,429515280,485235200,693838000,765358080,1078906000,1170170880
%N Theta series of laminated lattice LAMBDA_13^{mid}.
%C Theta series is an element of the space of modular forms on Gamma_1(8) with Kronecker character 8, weight 13/2, and dimension 7 over the integers. - _Andy Huchala_, May 04 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="/A006916/b006916.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/LAMBDA13_MID.html">Home page for this lattice</a>
%H <a href="/index/La#laminated">Index entries for sequences related to laminated lattices</a>
%o (Magma)
%o prec := 40;
%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,-1,0,-1,-1,1,0,1,0,1,1,0,0,4]);
%o L := LatticeWithGram(S);
%o T<q> := ThetaSeries(L,14);
%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 05 2023
%K nonn
%O 0,3
%A _N. J. A. Sloane_
%E a(11)-a(27) from _Andy Huchala_, May 05 2023
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