A047628 Theta series of 14-dimensional lattice Kappa_{14} with minimal norm 4.

1, 0, 1242, 11916, 72252, 266544, 807090, 2006856, 4603284, 8924940, 17571816, 30168396, 51799212, 82147608, 132245676, 191541024, 294596676, 410924988, 590219898, 800792568, 1123700904, 1442103768, 1991926080, 2519984088, 3314316426, 4155999192, 5427108108

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Theta series is an element of the space of modular forms on Gamma_1(18) with Kronecker character -3 in modulus 18, weight 7, and dimension 22 over the integers. - Andy Huchala, May 07 2023

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, A362875, A362876, A362877, A362878, A362879, A362880.

Programs

Magma

prec := 80;
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]);
L := LatticeWithGram(S);
T := ThetaSeries(L, 42);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
Coefficients(&+[Coefficients(T)[2*i-1]*B[i] :i in [1..22]]); // Andy Huchala, May 07 2023

Extensions

More terms from Andy Huchala, May 07 2023