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PROG
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(Magma)
prec := 20;
gram := [[6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 1, -2, 0, 0, 2, -2, 0, 0, 2], [0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 1, 0, -2, 0, 2, 0, -2, 0, 2], [0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 1, 0, 0, -2, 2, 0, 0, -2, 2], [0, 0, 0, 6, 2, 2, 2, 4, 2, 2, 2, 4, 1, 1, 1, 4, 2, 2, 2, 2, 2, 2, 2, 2], [2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, -1, 1, 1, 2, 2, 0, 0, 2], [0, 2, 0, 2, 0, 6, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 1, -1, 1, 2, 0, 2, 0, 2], [0, 0, 2, 2, 0, 0, 6, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 1, -1, 2, 0, 0, 2, 2], [0, 0, 0, 4, 0, 0, 0, 6, 2, 2, 2, 2, 0, 0, 0, 4, 2, 2, 2, 1, 2, 2, 2, 2], [2, 0, 0, 2, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, -1, 1, 1, 2], [0, 2, 0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 1, -1, 1, 2], [0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 6, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 1, -1, 2], [0, 0, 0, 4, 2, 2, 2, 2, 0, 0, 0, 6, 0, 0, 0, 4, 2, 2, 2, 2, 2, 2, 2, 1], [-2, 0, 0, 1, 2, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0], [0, -2, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0], [0, 0, -2, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0], [1, 1, 1, 4, 2, 2, 2, 4, 2, 2, 2, 4, 0, 0, 0, 6, 2, 2, 2, 4, 2, 2, 2, 4], [-2, 0, 0, 2, -1, 1, 1, 2, 2, 0, 0, 2, 2, 0, 0, 2, 6, 0, 0, 0, 0, 2, 2, 0], [0, -2, 0, 2, 1, -1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 2, 0, 2, 0], [0, 0, -2, 2, 1, 1, -1, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 6, 0, 2, 2, 0, 0], [2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4], [-2, 0, 0, 2, 2, 0, 0, 2, -1, 1, 1, 2, 2, 0, 0, 2, 0, 2, 2, 0, 6, 0, 0, 0], [0, -2, 0, 2, 0, 2, 0, 2, 1, -1, 1, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 6, 0, 0], [0, 0, -2, 2, 0, 0, 2, 2, 1, 1, -1, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 6, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 6]];
S := Matrix(gram);
L := LatticeWithGram(S);
T := ThetaSeriesModularForm(L);
Coefficients(PowerSeries(T, prec)); // Andy Huchala, May 14 2023
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