A362880 Theta series of 20-dimensional lattice Kappa_20.

1, 0, 15390, 575160, 7712820, 57281580, 296150580, 1184012640, 3944197800, 11364334080, 29395745478, 69157229760, 151652810580, 311116423500, 607158951120, 1127694969072, 2020055770530, 3478103852940, 5829999042420, 9467119804680, 15046034533560

Offset

0,3

Comments

Theta series is an element of the space of modular forms on Gamma_0(9) of weight 10 and dimension 11 over the integers.

References

J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Chap. 6.

Links

Andy Huchala, Table of n, a(n) for n = 0..20000

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

Example

G.f. = 1 + 15390*q^4 + 575160*q^6 + ...

Prog

(Magma)
prec := 40;
ls := [4, 2, 4, 0, -2, 4, 0, -2, 0, 4, 0, 0, -2, 0, 4, -2, -2, 0, 0, 0, 4, -2, -1, 1, 0, 0, 0, 4, -2, -1, 0, -1, 1, 2, 2, 4, -2, -2, 0, 1, 1, 2, 2, 2, 4, -2, 0, -2, 0, 1, 1, 0, 0, 0, 4, 1, 1, 0, 0, 0, -2, 0, -1, -1, -2, 4, -2, -1, 0, 0, 0, 1, 1, 1, 1, 1, -2, 4, 0, -1, 1, 1, 0, -1, 1, 0, 0, -1, 1, -1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, -1, 0, 0, 1, 1, 0, 1, 1, -1, 0, 0, 1, -1, 4, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 1, 4, 1, 0, -1, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 1, 0, 1, 0, 4];
S := SymmetricMatrix(ls);
L := LatticeWithGram(S);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
coeffs := [1, 0, 15390, 575160, 7712820, 57281580, 296150580, 1184012640, 3944197800, 11364334080, 29395745478];
Coefficients(&+[coeffs[i]*B[i] :i in [1..11]]);

Crossrefs

Cf. A029897, A047628, A362875, A362876, A362877, A362878, A362879.

Sequence in context: A054835 A182255 A054836 * A054837 A345562 A345817

Adjacent sequences: A362877 A362878 A362879 * A362881 A362882 A362883

Keyword

nonn

Author

Andy Huchala, May 08 2023

Status

approved