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Decomposition of \( S_{4}^{\mathrm{new}}(7) \) into irreducible Hecke orbits

magma: S := CuspForms(7,4);
magma: N := Newforms(S);
sage: N = Newforms(7,4,names="a")
Label Dimension Field $q$-expansion of eigenform
7.4.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(q^{2} \) \(\mathstrut-\) \(2q^{3} \) \(\mathstrut-\) \(7q^{4} \) \(\mathstrut+\) \(16q^{5} \) \(\mathstrut+\) \(2q^{6} \) \(\mathstrut-\) \(7q^{7} \) \(\mathstrut+\) \(15q^{8} \) \(\mathstrut-\) \(23q^{9} \) \(\mathstrut+O(q^{10}) \)