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Decomposition of \( S_{10}^{\mathrm{new}}(9) \) into irreducible Hecke orbits

magma: S := CuspForms(9,10);
magma: N := Newforms(S);
sage: N = Newforms(9,10,names="a")
Label Dimension Field $q$-expansion of eigenform
9.10.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(18q^{2} \) \(\mathstrut-\) \(188q^{4} \) \(\mathstrut+\) \(1530q^{5} \) \(\mathstrut+\) \(9128q^{7} \) \(\mathstrut+\) \(12600q^{8} \) \(\mathstrut+O(q^{10}) \)
9.10.1.b 1 \(\Q\) \(q \) \(\mathstrut-\) \(512q^{4} \) \(\mathstrut-\) \(12580q^{7} \) \(\mathstrut+O(q^{10}) \)
9.10.1.c 1 \(\Q\) \(q \) \(\mathstrut+\) \(36q^{2} \) \(\mathstrut+\) \(784q^{4} \) \(\mathstrut+\) \(1314q^{5} \) \(\mathstrut-\) \(4480q^{7} \) \(\mathstrut+\) \(9792q^{8} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{10}^{\mathrm{old}}(9) \) into lower level spaces

\( S_{10}^{\mathrm{old}}(9) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/3/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(3)) }^{\oplus 2 } $