A033696 - OEIS

A033696

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

1, 0, 144, 768, 5256, 9216, 38208, 50688, 167688, 178176, 487008, 481536, 1282464, 1115136, 2623104, 2290176, 5365512, 4257792, 9250896, 7425792, 16430256, 12300288, 25117632, 19321344, 40915872, 29306880, 57926880, 43212288, 88342848, 61535232, 118995840

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OFFSET

0,3

COMMENTS

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

LINKS

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

Index entries for sequences related to D_4 lattice

PROG

(Magma)

prec := 30;

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];

S := Matrix(12, basis);

L := LatticeWithBasis(S);

T := ThetaSeriesModularForm(L);

Coefficients(PowerSeries(T, prec)); // Andy Huchala, May 15 2023

CROSSREFS

Sequence in context: A233903 A233897 A250428 * A233653 A233646 A268806

Adjacent sequences: A033693 A033694 A033695 * A033697 A033698 A033699

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Andy Huchala, May 15 2023

STATUS

approved