A033698 - OEIS

%I #17 Jul 08 2025 19:56:55

%S 1,0,216,1440,7290,17280,50436,116640,186408,366912,714420,895104,

%T 1600812,2566080,3070656,4734720,7501410,7858944,12134340,17146080,

%U 18299952,25463232,36770760,35652096,51224508,67651200,67882320,89316576,122996880,113574528

%N Theta series of lattice A_2 tensor E_6 (dimension 12, det. 6561, min. norm 4).

%C This theta series is an element of the space of modular forms on Gamma_0(36) of weight 6 and dimension 36. - _Andy Huchala_, May 17 2023

%H Andy Huchala, <a href="/A033698/b033698.txt">Table of n, a(n) for n = 0..10000</a>

%o (Magma)

%o prec := 30;

%o basis := [1,-1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,1,-1,0,0,1,-1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,1,-1,2,-2,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,2,-2,0,0,0,0,0,0,0,0,0];

%o S := Matrix(24,basis);

%o L := LatticeWithBasis(S);

%o T := ThetaSeriesModularForm(L); // takes a minute

%o coeffs := Coefficients(PowerSeries(T,prec*4));

%o [coeffs[4*i+1] : i in [0..prec-1]]; // _Andy Huchala_, May 17 2023

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Andy Huchala_, May 17 2023