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Decomposition of \( S_{6}^{\mathrm{new}}(18) \) into irreducible Hecke orbits

magma: S := CuspForms(18,6);
magma: N := Newforms(S);
sage: N = Newforms(18,6,names="a")
Label Dimension Field $q$-expansion of eigenform
18.6.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(4q^{2} \) \(\mathstrut+\) \(16q^{4} \) \(\mathstrut-\) \(96q^{5} \) \(\mathstrut-\) \(148q^{7} \) \(\mathstrut-\) \(64q^{8} \) \(\mathstrut+O(q^{10}) \)
18.6.1.b 1 \(\Q\) \(q \) \(\mathstrut-\) \(4q^{2} \) \(\mathstrut+\) \(16q^{4} \) \(\mathstrut+\) \(66q^{5} \) \(\mathstrut+\) \(176q^{7} \) \(\mathstrut-\) \(64q^{8} \) \(\mathstrut+O(q^{10}) \)
18.6.1.c 1 \(\Q\) \(q \) \(\mathstrut+\) \(4q^{2} \) \(\mathstrut+\) \(16q^{4} \) \(\mathstrut+\) \(96q^{5} \) \(\mathstrut-\) \(148q^{7} \) \(\mathstrut+\) \(64q^{8} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{6}^{\mathrm{old}}(18) \) into lower level spaces

\( S_{6}^{\mathrm{old}}(18) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/9/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(9)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/6/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(6)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/3/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(3)) }^{\oplus 4 } $