A033692 - OEIS

A033692

Theta series of lattice D_4 tensor D_4 (dimension 16, det. 65536, min. norm 4).

1, 0, 288, 3072, 38880, 110592, 654720, 1161216, 4964832, 6758400, 23385024, 27509760, 84872832, 88584192, 246470400, 241330176, 635597280, 579280896, 1432192416, 1261992960, 3030460992, 2543861760, 5832383616, 4806715392, 10864625280, 8616886272, 18780246720

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OFFSET

0,3

COMMENTS

This theta series is an element of the space of modular forms on Gamma_0(4) of weight 8 and dimension 5. - 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, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 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, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1];

S := Matrix(16, basis);

L := LatticeWithBasis(S);

T := ThetaSeriesModularForm(L);

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

CROSSREFS

Sequence in context: A049230 A322677 A235552 * A182026 A229506 A332429

Adjacent sequences: A033689 A033690 A033691 * A033693 A033694 A033695

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Andy Huchala, May 15 2023

STATUS

approved