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Decomposition of \( S_{10}^{\mathrm{new}}(3) \) into irreducible Hecke orbits

magma: S := CuspForms(3,10);
magma: N := Newforms(S);
sage: N = Newforms(3,10,names="a")
Label Dimension Field $q$-expansion of eigenform
3.10.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(36q^{2} \) \(\mathstrut-\) \(81q^{3} \) \(\mathstrut+\) \(784q^{4} \) \(\mathstrut-\) \(1314q^{5} \) \(\mathstrut+\) \(2916q^{6} \) \(\mathstrut-\) \(4480q^{7} \) \(\mathstrut-\) \(9792q^{8} \) \(\mathstrut+\) \(6561q^{9} \) \(\mathstrut+O(q^{10}) \)
3.10.1.b 1 \(\Q\) \(q \) \(\mathstrut+\) \(18q^{2} \) \(\mathstrut+\) \(81q^{3} \) \(\mathstrut-\) \(188q^{4} \) \(\mathstrut-\) \(1530q^{5} \) \(\mathstrut+\) \(1458q^{6} \) \(\mathstrut+\) \(9128q^{7} \) \(\mathstrut-\) \(12600q^{8} \) \(\mathstrut+\) \(6561q^{9} \) \(\mathstrut+O(q^{10}) \)