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Decomposition of \( S_{6}^{\mathrm{new}}(3) \) into irreducible Hecke orbits

magma: S := CuspForms(3,6);
magma: N := Newforms(S);
sage: N = Newforms(3,6,names="a")
Label Dimension Field $q$-expansion of eigenform
3.6.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(6q^{2} \) \(\mathstrut+\) \(9q^{3} \) \(\mathstrut+\) \(4q^{4} \) \(\mathstrut+\) \(6q^{5} \) \(\mathstrut-\) \(54q^{6} \) \(\mathstrut-\) \(40q^{7} \) \(\mathstrut+\) \(168q^{8} \) \(\mathstrut+\) \(81q^{9} \) \(\mathstrut+O(q^{10}) \)