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, 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