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A047628 Theta series of 14-dimensional lattice Kappa_{14} with minimal norm 4.

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%I A047628 #27 May 10 2023 05:19:58
%S A047628 1,0,1242,11916,72252,266544,807090,2006856,4603284,8924940,17571816,
%T A047628 30168396,51799212,82147608,132245676,191541024,294596676,410924988,
%U A047628 590219898,800792568,1123700904,1442103768,1991926080,2519984088,3314316426,4155999192,5427108108
%N A047628 Theta series of 14-dimensional lattice Kappa_{14} with minimal norm 4.
%C A047628 Theta series is an element of the space of modular forms on Gamma_1(18) with Kronecker character -3 in modulus 18, weight 7, and dimension 22 over the integers. - _Andy Huchala_, May 07 2023
%D A047628 J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Chap. 6.
%H A047628 Andy Huchala, <a href="/A047628/b047628.txt">Table of n, a(n) for n = 0..20000</a>
%H A047628 G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/KAPPA14.1.html">Home page for this lattice</a>
%o A047628 (Magma)
%o A047628 prec := 80;
%o A047628 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]);
%o A047628 L := LatticeWithGram(S);
%o A047628 T<q> := ThetaSeries(L, 42);
%o A047628 M := ThetaSeriesModularFormSpace(L);
%o A047628 B := Basis(M, prec);
%o A047628 Coefficients(&+[Coefficients(T)[2*i-1]*B[i] :i in [1..22]]); // _Andy Huchala_, May 07 2023
%Y A047628 Cf. A029897, A362875, A362876, A362877, A362878, A362879, A362880.
%K A047628 nonn
%O A047628 0,3
%A A047628 _N. J. A. Sloane_
%E A047628 More terms from _Andy Huchala_, May 07 2023