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Decomposition of \( S_{4}^{\mathrm{new}}(15) \) into irreducible Hecke orbits

magma: S := CuspForms(15,4);
magma: N := Newforms(S);
sage: N = Newforms(15,4,names="a")
Label Dimension Field $q$-expansion of eigenform
15.4.1.a 1 \(\Q\) \(q \) \(\mathstrut+\) \(q^{2} \) \(\mathstrut+\) \(3q^{3} \) \(\mathstrut-\) \(7q^{4} \) \(\mathstrut+\) \(5q^{5} \) \(\mathstrut+\) \(3q^{6} \) \(\mathstrut-\) \(24q^{7} \) \(\mathstrut-\) \(15q^{8} \) \(\mathstrut+\) \(9q^{9} \) \(\mathstrut+O(q^{10}) \)
15.4.1.b 1 \(\Q\) \(q \) \(\mathstrut+\) \(3q^{2} \) \(\mathstrut-\) \(3q^{3} \) \(\mathstrut+\) \(q^{4} \) \(\mathstrut-\) \(5q^{5} \) \(\mathstrut-\) \(9q^{6} \) \(\mathstrut+\) \(20q^{7} \) \(\mathstrut-\) \(21q^{8} \) \(\mathstrut+\) \(9q^{9} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{4}^{\mathrm{old}}(15) \) into lower level spaces

\( S_{4}^{\mathrm{old}}(15) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/5/4/1/ }{ S^{ new }_{ 4 }(\Gamma_0(5)) }^{\oplus 2 } $