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Decomposition of \( S_{6}^{\mathrm{new}}(9) \) into irreducible Hecke orbits

magma: S := CuspForms(9,6);
magma: N := Newforms(S);
sage: N = Newforms(9,6,names="a")
Label Dimension Field $q$-expansion of eigenform
9.6.1.a 1 \(\Q\) \(q \) \(\mathstrut+\) \(6q^{2} \) \(\mathstrut+\) \(4q^{4} \) \(\mathstrut-\) \(6q^{5} \) \(\mathstrut-\) \(40q^{7} \) \(\mathstrut-\) \(168q^{8} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{6}^{\mathrm{old}}(9) \) into lower level spaces

\( S_{6}^{\mathrm{old}}(9) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/3/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(3)) }^{\oplus 2 } $