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PROG
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(Magma)
prec := 20;
gram := [[6, 0, 0, 0, 2, 2, -2, 1, 1, 1, 0, 0], [0, 6, 0, 0, 2, 2, 1, -2, 1, 1, 0, 0], [0, 0, 6, 0, 2, 2, 1, 1, -2, 1, 0, 0], [0, 0, 0, 6, 2, 2, 1, 1, 1, -2, 0, 0], [2, 2, 2, 2, 6, 4, 2, 2, 2, 2, 1, 4], [2, 2, 2, 2, 4, 6, 2, 2, 2, 2, 4, 1], [-2, 1, 1, 1, 2, 2, 6, 0, 0, 0, 2, 2], [1, -2, 1, 1, 2, 2, 0, 6, 0, 0, 2, 2], [1, 1, -2, 1, 2, 2, 0, 0, 6, 0, 2, 2], [1, 1, 1, -2, 2, 2, 0, 0, 0, 6, 2, 2], [0, 0, 0, 0, 1, 4, 2, 2, 2, 2, 6, 0], [0, 0, 0, 0, 4, 1, 2, 2, 2, 2, 0, 6]];
S := Matrix(gram);
L := LatticeWithGram(S);
T<q> := ThetaSeries(L, 14);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
Coefficients(&+[Coefficients(T)[2*i-1]*B[i] :i in [1..7]]); // Andy Huchala, May 14 2023
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