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%I #15 May 16 2023 05:18:12
%S 1,0,288,3072,38880,110592,654720,1161216,4964832,6758400,23385024,
%T 27509760,84872832,88584192,246470400,241330176,635597280,579280896,
%U 1432192416,1261992960,3030460992,2543861760,5832383616,4806715392,10864625280,8616886272,18780246720
%N Theta series of lattice D_4 tensor D_4 (dimension 16, det. 65536, min. norm 4).
%C This theta series is an element of the space of modular forms on Gamma_0(4) of weight 8 and dimension 5. - _Andy Huchala_, May 15 2023
%H Andy Huchala, <a href="/A033692/b033692.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Da#D4">Index entries for sequences related to D_4 lattice</a>
%o (Magma)
%o prec := 30;
%o basis := [1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,1,-1,0,0,0,0,0,0,0,0,1,1,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1];
%o S := Matrix(16,basis);
%o L := LatticeWithBasis(S);
%o T := ThetaSeriesModularForm(L);
%o Coefficients(PowerSeries(T,prec)); // _Andy Huchala_, May 15 2023
%K nonn
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _Andy Huchala_, May 15 2023