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Decomposition of \( S_{4}^{\mathrm{new}}(18) \) into irreducible Hecke orbits

magma: S := CuspForms(18,4);
magma: N := Newforms(S);
sage: N = Newforms(18,4,names="a")
Label Dimension Field $q$-expansion of eigenform
18.4.1.a 1 \(\Q\) \(q \) \(\mathstrut+\) \(2q^{2} \) \(\mathstrut+\) \(4q^{4} \) \(\mathstrut-\) \(6q^{5} \) \(\mathstrut-\) \(16q^{7} \) \(\mathstrut+\) \(8q^{8} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{4}^{\mathrm{old}}(18) \) into lower level spaces

\( S_{4}^{\mathrm{old}}(18) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/9/4/1/ }{ S^{ new }_{ 4 }(\Gamma_0(9)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/6/4/1/ }{ S^{ new }_{ 4 }(\Gamma_0(6)) }^{\oplus 2 } $