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PROG
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(Magma)
prec := 10;
ls := [4, 0, 4, 0, 0, 4, 2, 2, 2, 4, 0, 0, -2, -1, 4, 0, 0, 0, 1, 0, 4, 2, 0, 0, 1, 0, 0, 4, 1, -1, -1, 0, 2, 2, 2, 4, 1, -1, -1, 0, 1, 1, 1, 1, 4, 1, 1, 1, 2, -1, 1, -1, -1, 0, 4, 1, -1, 1, 0, -1, 1, 1, 1, 0, 0, 4, 1, -1, 1, 1, 0, 2, 0, 1, 2, 2, 2, 4, -1, 1, 1, 0, -1, -1, -1, -2, -2, 0, 0, -1, 4, -1, -1, -1, -2, 1, -1, -1, 0, 0, -2, 0, -1, 0, 4, -1, 1, -1, 0, 1, 1, -1, 0, 0, 0, -2, -1, 0, 0, 4, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -2, 2, 2, 2, 4, 1, -1, 1, 1, 0, 0, 0, 0, 1, 1, -1, 1, -2, 0, 0, -1, 4, 1, 1, 1, 1, 0, 0, 0, 0, -1, 1, 1, 1, 0, -2, 0, -1, 0, 4, -1, -1, 1, -1, 0, 0, 0, 0, 1, -1, 1, 1, 0, 0, -2, -1, 0, 0, 4, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -2, 2, 2, 2, 4];
S := SymmetricMatrix(ls);
L := LatticeWithGram(S);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
coeffs := [1, 0, 3960];
Coefficients(&+[coeffs[i]*B[i] :i in [1..3]]); // Andy Huchala, May 13 2023
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