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Decomposition of \( S_{8}^{\mathrm{new}}(12) \) into irreducible Hecke orbits

magma: S := CuspForms(12,8);
magma: N := Newforms(S);
sage: N = Newforms(12,8,names="a")
Label Dimension Field $q$-expansion of eigenform
12.8.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(27q^{3} \) \(\mathstrut-\) \(378q^{5} \) \(\mathstrut-\) \(832q^{7} \) \(\mathstrut+\) \(729q^{9} \) \(\mathstrut+O(q^{10}) \)
12.8.1.b 1 \(\Q\) \(q \) \(\mathstrut+\) \(27q^{3} \) \(\mathstrut+\) \(270q^{5} \) \(\mathstrut+\) \(1112q^{7} \) \(\mathstrut+\) \(729q^{9} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{8}^{\mathrm{old}}(12) \) into lower level spaces

\( S_{8}^{\mathrm{old}}(12) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/6/8/1/ }{ S^{ new }_{ 8 }(\Gamma_0(6)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/3/8/1/ }{ S^{ new }_{ 8 }(\Gamma_0(3)) }^{\oplus 3 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/2/8/1/ }{ S^{ new }_{ 8 }(\Gamma_0(2)) }^{\oplus 4 } $