A033698 Theta series of lattice A_2 tensor E_6 (dimension 12, det. 6561, min. norm 4).

1, 0, 216, 1440, 7290, 17280, 50436, 116640, 186408, 366912, 714420, 895104, 1600812, 2566080, 3070656, 4734720, 7501410, 7858944, 12134340, 17146080, 18299952, 25463232, 36770760, 35652096, 51224508, 67651200, 67882320, 89316576, 122996880, 113574528

Offset

0,3

Comments

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

Links

Andy Huchala, Table of n, a(n) for n = 0..10000

Prog

(Magma)
prec := 30;
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];
S := Matrix(24, basis);
L := LatticeWithBasis(S);
T := ThetaSeriesModularForm(L); // takes a minute
coeffs := Coefficients(PowerSeries(T, prec*4));
[coeffs[4*i+1] : i in [0..prec-1]]; // Andy Huchala, May 17 2023

Crossrefs

Sequence in context: A233980 A233974 A016863 * A121683 A016911 A370693

Adjacent sequences: A033695 A033696 A033697 * A033699 A033700 A033701

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Andy Huchala, May 17 2023

Status

approved