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Decomposition of \( S_{6}^{\mathrm{new}}(16) \) into irreducible Hecke orbits

magma: S := CuspForms(16,6);
magma: N := Newforms(S);
sage: N = Newforms(16,6,names="a")
Label Dimension Field $q$-expansion of eigenform
16.6.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(20q^{3} \) \(\mathstrut-\) \(74q^{5} \) \(\mathstrut+\) \(24q^{7} \) \(\mathstrut+\) \(157q^{9} \) \(\mathstrut+O(q^{10}) \)
16.6.1.b 1 \(\Q\) \(q \) \(\mathstrut+\) \(12q^{3} \) \(\mathstrut+\) \(54q^{5} \) \(\mathstrut+\) \(88q^{7} \) \(\mathstrut-\) \(99q^{9} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{6}^{\mathrm{old}}(16) \) into lower level spaces

\( S_{6}^{\mathrm{old}}(16) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/8/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(8)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/4/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(4)) }^{\oplus 3 } $