A033696 - OEIS

%I #12 May 16 2023 06:57:53

%S 1,0,144,768,5256,9216,38208,50688,167688,178176,487008,481536,

%T 1282464,1115136,2623104,2290176,5365512,4257792,9250896,7425792,

%U 16430256,12300288,25117632,19321344,40915872,29306880,57926880,43212288,88342848,61535232,118995840

%N Theta series of lattice D_3 tensor D_4 (dimension 12, det. 16384, min. norm 4).

%C This theta series is an element of the space of modular forms on Gamma_0(8) of weight 6 and dimension 7. - _Andy Huchala_, May 15 2023

%H Andy Huchala, <a href="/A033696/b033696.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 := [1,1,0,0,1,1,0,0,0,0,0,0,1,-1,0,0,1,-1,0,0,0,0,0,0,0,1,-1,0,0,1,-1,0,0,0,0,0,0,0,1,-1,0,0,1,-1,0,0,0,0,1,1,0,0,-1,-1,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,0,1,1,0,0,-1,-1,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,1,-1,0,0,-1,1];

%o S := Matrix(12,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