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Decomposition of \( S_{4}^{\mathrm{new}}(10) \) into irreducible Hecke orbits

magma: S := CuspForms(10,4);
magma: N := Newforms(S);
sage: N = Newforms(10,4,names="a")
Label Dimension Field $q$-expansion of eigenform
10.4.1.a 1 \(\Q\) \(q \) \(\mathstrut+\) \(2q^{2} \) \(\mathstrut-\) \(8q^{3} \) \(\mathstrut+\) \(4q^{4} \) \(\mathstrut+\) \(5q^{5} \) \(\mathstrut-\) \(16q^{6} \) \(\mathstrut-\) \(4q^{7} \) \(\mathstrut+\) \(8q^{8} \) \(\mathstrut+\) \(37q^{9} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{4}^{\mathrm{old}}(10) \) into lower level spaces

\( S_{4}^{\mathrm{old}}(10) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/5/4/1/ }{ S^{ new }_{ 4 }(\Gamma_0(5)) }^{\oplus 2 } $