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Decomposition of \( S_{12}^{\mathrm{new}}(1) \) into irreducible Hecke orbits

magma: S := CuspForms(1,12);
magma: N := Newforms(S);
sage: N = Newforms(1,12,names="a")
Label Dimension Field $q$-expansion of eigenform
1.12.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(24q^{2} \) \(\mathstrut+\) \(252q^{3} \) \(\mathstrut-\) \(1472q^{4} \) \(\mathstrut+\) \(4830q^{5} \) \(\mathstrut-\) \(6048q^{6} \) \(\mathstrut-\) \(16744q^{7} \) \(\mathstrut+\) \(84480q^{8} \) \(\mathstrut-\) \(113643q^{9} \) \(\mathstrut+O(q^{10}) \)