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A362880 Theta series of 20-dimensional lattice Kappa_20.

%I A362880 #15 May 13 2023 01:56:41
%S A362880 1,0,15390,575160,7712820,57281580,296150580,1184012640,3944197800,
%T A362880 11364334080,29395745478,69157229760,151652810580,311116423500,
%U A362880 607158951120,1127694969072,2020055770530,3478103852940,5829999042420,9467119804680,15046034533560
%N A362880 Theta series of 20-dimensional lattice Kappa_20.
%C A362880 Theta series is an element of the space of modular forms on Gamma_0(9) of weight 10 and dimension 11 over the integers.
%D A362880 J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Chap. 6.
%H A362880 Andy Huchala, <a href="/A362880/b362880.txt">Table of n, a(n) for n = 0..20000</a>
%H A362880 G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/KAPPA20.html">Home page for this lattice</a>.
%e A362880 G.f. = 1 + 15390*q^4 + 575160*q^6 + ...
%o A362880 (Magma)
%o A362880 prec := 40;
%o A362880 ls := [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,-1,4,0,0,0,0,0,0,0,0,0,0,0,0,-2,4,0,-1,0,0,1,1,0,1,1,-1,0,0,1,-1,4,0,0,1,0,-1,0,1,0,0,0,-1,0,0,1,0,4,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,0,1,4,1,0,-1,1,1,0,-1,-1,0,0,0,0,0,0,1,-1,0,1,4,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,1,0,1,0,4];
%o A362880 S := SymmetricMatrix(ls);
%o A362880 L := LatticeWithGram(S);
%o A362880 M := ThetaSeriesModularFormSpace(L);
%o A362880 B := Basis(M, prec);
%o A362880 coeffs := [1, 0, 15390, 575160, 7712820, 57281580, 296150580, 1184012640, 3944197800, 11364334080, 29395745478];
%o A362880 Coefficients(&+[coeffs[i]*B[i] :i in [1..11]]);
%Y A362880 Cf. A029897, A047628, A362875, A362876, A362877, A362878, A362879.
%K A362880 nonn
%O A362880 0,3
%A A362880 _Andy Huchala_, May 08 2023