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Theta series of lattice D3 tensor D3 (dimension 9, det. 4096, min. norm 4).
1

%I #16 May 16 2023 06:57:34

%S 1,0,72,192,864,1152,3168,3456,10674,8448,18432,17856,42816,31104,

%T 61056,51072,118224,80640,146376,115776,258624,166656,291744,233856,

%U 492576,304128,534528,403200,819072,521856,874368,642816,1372914,814848,1334016,1008000

%N Theta series of lattice D3 tensor D3 (dimension 9, det. 4096, min. norm 4).

%C This theta series is an element of the space of modular forms on Gamma_1(32) with Kronecker character 8 in modulus 32, weight 9/2, and dimension 18. - _Andy Huchala_, May 16 2023

%H Andy Huchala, <a href="/A033693/b033693.txt">Table of n, a(n) for n = 0..10000</a>

%o (Magma)

%o prec := 30;

%o basis := [1,1,0,1,1,0,0,0,0,1,-1,0,1,-1,0,0,0,0,0,1,-1,0,1,-1,0,0,0,1,1,0,-1,-1,0,0,0,0,1,-1,0,-1,1,0,0,0,0,0,1,-1,0,-1,1,0,0,0,0,0,0,1,1,0,-1,-1,0,0,0,0,1,-1,0,-1,1,0,0,0,0,0,1,-1,0,-1,1];

%o S := Matrix(9,basis);

%o L := LatticeWithBasis(S);

%o T := ThetaSeriesModularForm(L);

%o Coefficients(PowerSeries(T,prec)); // _Andy Huchala_, May 16 2023

%K nonn

%O 0,3

%A _N. J. A. Sloane_.

%E a(21)-a(31) from _Sean A. Irvine_, Jul 13 2020

%E More terms from _Andy Huchala_, May 16 2023