|
PROG
|
(Magma)
prec := 20;
ls := [[4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 4, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -2, 4, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 1, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, -2, -2, 4, 1, -2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 1, 4, -2, -2, 1, 0, 0, -2, 1], [0, 0, 0, 0, 1, -2, -2, 4, 1, -2, 0, 0, 1, -2], [0, 0, 0, 0, 0, 0, -2, 1, 4, -2, -2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, -2, -2, 4, 1, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 4, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, 4, 0, 0], [0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 4, -2], [0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -2, 4]];
S := Matrix(ls);
L := LatticeWithGram(S);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
coeffs := [1, 0, 378, 4032, 24948, 84672, 272706, 689472];
Coefficients(&+[coeffs[i]*B[i] :i in [1..8]]); // Andy Huchala, May 13 2023
|