A033693 Theta series of lattice D3 tensor D3 (dimension 9, det. 4096, min. norm 4).

1, 0, 72, 192, 864, 1152, 3168, 3456, 10674, 8448, 18432, 17856, 42816, 31104, 61056, 51072, 118224, 80640, 146376, 115776, 258624, 166656, 291744, 233856, 492576, 304128, 534528, 403200, 819072, 521856, 874368, 642816, 1372914, 814848, 1334016, 1008000

Offset

0,3

Comments

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

Links

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

Prog

(Magma)
prec := 30;
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];
S := Matrix(9, basis);
L := LatticeWithBasis(S);
T := ThetaSeriesModularForm(L);
Coefficients(PowerSeries(T, prec)); // Andy Huchala, May 16 2023

Crossrefs

Sequence in context: A254437 A304376 A028977 * A250786 A302886 A235186

Adjacent sequences: A033690 A033691 A033692 * A033694 A033695 A033696

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

a(21)-a(31) from Sean A. Irvine, Jul 13 2020

More terms from Andy Huchala, May 16 2023

Status

approved