A033288 Theta series of 20-dimensional lattice L_20 with group 2.M_22.2.

1, 0, 0, 0, 6160, 27104, 157080, 633600, 2152920, 6049120, 15601432, 37243360, 81265800, 166554080, 325036800, 603357216, 1082004000, 1863350720, 3121660080, 5069606080, 8058310568, 12471782400, 19002534320, 28292374880, 41585775000, 59922289504, 85450069320

Offset

0,5

Comments

This theta series is an element of the space of modular forms on Gamma_0(7) of weight 10 and dimension 7. - Andy Huchala, May 15 2023

References

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. 39.

Links

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

G. Nebe and N. J. A. Sloane, Home page for this lattice

Prog

(Magma)
prec := 30;
gram := [8, 2, 8, -1, 0, 8, 0, -2, 0, 8, 2, -1, -2, 4, 8, -2, 0, -1, -1, -1, 8, -2, -1, 0, -1, -2, 0, 8, 0, -1, 0, -1, -2, -2, -1, 8, 0, 0, -1, -2, -1, 0, 0, -1, 8, 1, 1, 0, 2, 2, 0, 0, 0, 0, 8, 1, 4, 2, -2, -1, -2, -2, 2, -2, 0, 8, -4, -2, 2, 0, 0, 0, -1, -1, 1, 0, -1, 8, 4, 0, -1, 0, 1, -2, 2, 0, -1, -2, 1, -4, 8, -4, 1, 0, -1, 0, -1, 0, 0, -1, -1, 2, 2, 0, 8, -2, -2, -4, 4, 2, 0, 2, -1, -2, 0, -2, 0, 0, -1, 8, 4, 1, -2, 2, 2, 2, -2, -2, -1, -1, -1, -4, 4, -2, 1, 8, 2, -1, -2, -1, 0, 0, -1, -2, -1, -2, -2, -1, 0, -2, 2, 2, 8, -2, 0, 0, -2, -2, -1, 1, 0, 0, -1, 2, 1, -1, 0, 2, -2, 2, 8, 0, 0, -1, -2, -1, 0, 0, 2, 4, -4, -2, -1, 0, -1, -2, 0, 0, 1, 8, 4, 1, -1, -2, 1, -2, 1, -4, 0, -2, 1, -1, 4, 0, 0, 2, 4, 2, -1, 8];
S := SymmetricMatrix(gram);
L := LatticeWithGram(S);
T := ThetaSeriesModularForm(L);
Coefficients(PowerSeries(T, prec)); // Andy Huchala, May 15 2023

Crossrefs

Sequence in context: A318251 A281265 A007992 * A266586 A057880 A151967

Adjacent sequences: A033285 A033286 A033287 * A033289 A033290 A033291

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Andy Huchala, May 15 2023

Status

approved