A362876 Theta series of 16-dimensional lattice Kappa_16.

1, 0, 2772, 42624, 335052, 1545984, 5698860, 16297344, 42785244, 94440960, 204094296, 385391232, 730053060, 1240934400, 2151268128, 3374469504, 5476016700, 8115545088, 12477938100, 17677480320, 26111897640, 35570481408, 50909418000, 67336722432, 93433877268

Offset: 0

Author

Andy Huchala, May 07 2023

Keywords

• nonn

Comments

Theta series is an element of the space of modular forms on Gamma_0(12) of weight 8 and dimension 17 over the integers.

Examples

			G.f. = 1 + 2772*q^4 + 42624*q^6 + ...
		

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.

Crossrefs

Cf. A029897, A047628, A362875, A362877, A362878, A362879, A362880.

Programs

Magma

prec := 40;
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]);
L := LatticeWithGram(S);
T := ThetaSeries(L, 32);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M,prec);
Coefficients(&+[Coefficients(T)[2*i-1]*B[i] : i in [1..17]]);