%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