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A047628
Theta series of 14-dimensional lattice Kappa_{14} with minimal norm 4.
8
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
0,3
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
G. Nebe and N. J. A. Sloane, Home page for this lattice
PROG
(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<q> := 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
KEYWORD
nonn
EXTENSIONS
More terms from Andy Huchala, May 07 2023
STATUS
approved