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A362877 Theta series of 17-dimensional lattice Kappa_17.

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%I A362877 #15 May 10 2023 05:19:38
%S A362877 1,0,4266,81792,737862,3809280,15406210,47505792,133390290,312588288,
%T A362877 711232812,1408787328,2789963820,4931371008,8870944884,14417119872,
%U A362877 24144502662,36878456832,58393537998,84926534016
%N A362877 Theta series of 17-dimensional lattice Kappa_17.
%C A362877 Theta series is an element of the space of modular forms on Gamma_1(48) with Kronecker character 12 in modulus 48, weight 17/2, and dimension 66 over the integers.
%D A362877 J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Chap. 6.
%H A362877 G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/KAPPA17.1.html">Home page for this lattice</a>.
%e A362877 G.f. = 1 + 4266*q^4 + 81792*q^6 + ...
%o A362877 (Magma)
%o A362877 prec := 10;
%o A362877 S := SymmetricMatrix([4,2,4,0,-2,4,0,-2,0,4,0,0,-2,0,4,-2,-2,0,0,0,4,-2,-1,1,0,0,0,4,-2,-1,0,-1,1,2,2,4,-2,-2,0,1,1,2,2,2,4,-2,0,-2,0,1,1,0,0,0,4,1,1,0,0,0,-2,0,-1,-1,-2,4,-2,-1,0,0,0,1,1,1,1,1,-2,4,0,-1,1,1,0,-1,1,0,0,-1,1,-1,4,0,0,0,0,0,0,1,0,1,-1,1,-1,1,4,0,0,0,0,-1,1,-1,0,0,0,-1,0,0,-1,4,-1,0,0,-1,0,0,0,0,0,1,-1,1,0,0,-1,4,0,0,0,0,0,0,0,1,0,-1,1,-1,1,0,1,-1,4]);
%o A362877 L := LatticeWithGram(S);
%o A362877 T<q> := ThetaSeries(L, 2*prec);
%o A362877 [Coefficients(T)[2*i-1] : i in [1..prec]];
%Y A362877 Cf. A029897, A047628, A362875, A362876, A362878, A362879, A362880.
%K A362877 nonn
%O A362877 0,3
%A A362877 _Andy Huchala_, May 07 2023