A362877 Theta series of 17-dimensional lattice Kappa_17.

1, 0, 4266, 81792, 737862, 3809280, 15406210, 47505792, 133390290, 312588288, 711232812, 1408787328, 2789963820, 4931371008, 8870944884, 14417119872, 24144502662, 36878456832, 58393537998, 84926534016

Offset: 0

Author

Andy Huchala, May 07 2023

Keywords

• nonn

Comments

Theta series is an element of the space of modular forms on Gamma_1(48) with Kronecker character 12 in modulus 48, weight 17/2, and dimension 66 over the integers.

Examples

			G.f. = 1 + 4266*q^4 + 81792*q^6 + ...
		

References

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

Links

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

Crossrefs

Cf. A029897, A047628, A362875, A362876, A362878, A362879, A362880.

Programs

Magma

prec := 10;
S := SymmetricMatrix([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,-1,4,0,0,0,0,0,0,1,0,1,-1,1,-1,1,4,0,0,0,0,-1,1,-1,0,0,0,-1,0,0,-1,4,-1,0,0,-1,0,0,0,0,0,1,-1,1,0,0,-1,4,0,0,0,0,0,0,0,1,0,-1,1,-1,1,0,1,-1,4]);
L := LatticeWithGram(S);
T := ThetaSeries(L, 2*prec);
[Coefficients(T)[2*i-1] : i in [1..prec]];