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Decomposition of \( S_{2}^{\mathrm{new}}(19) \) into irreducible Hecke orbits

magma: S := CuspForms(19,2);
magma: N := Newforms(S);
sage: N = Newforms(19,2,names="a")
Label Dimension Field $q$-expansion of eigenform
19.2.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(2q^{3} \) \(\mathstrut-\) \(2q^{4} \) \(\mathstrut+\) \(3q^{5} \) \(\mathstrut-\) \(q^{7} \) \(\mathstrut+\) \(q^{9} \) \(\mathstrut+O(q^{10}) \)