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Decomposition of \( S_{4}^{\mathrm{new}}(6) \) into irreducible Hecke orbits

magma: S := CuspForms(6,4);
magma: N := Newforms(S);
sage: N = Newforms(6,4,names="a")
Label Dimension Field $q$-expansion of eigenform
6.4.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(2q^{2} \) \(\mathstrut-\) \(3q^{3} \) \(\mathstrut+\) \(4q^{4} \) \(\mathstrut+\) \(6q^{5} \) \(\mathstrut+\) \(6q^{6} \) \(\mathstrut-\) \(16q^{7} \) \(\mathstrut-\) \(8q^{8} \) \(\mathstrut+\) \(9q^{9} \) \(\mathstrut+O(q^{10}) \)