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Decomposition of \( S_{6}^{\mathrm{new}}(24) \) into irreducible Hecke orbits

magma: S := CuspForms(24,6);
magma: N := Newforms(S);
sage: N = Newforms(24,6,names="a")
Label Dimension Field $q$-expansion of eigenform
24.6.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(9q^{3} \) \(\mathstrut-\) \(34q^{5} \) \(\mathstrut-\) \(240q^{7} \) \(\mathstrut+\) \(81q^{9} \) \(\mathstrut+O(q^{10}) \)
24.6.1.b 1 \(\Q\) \(q \) \(\mathstrut-\) \(9q^{3} \) \(\mathstrut+\) \(94q^{5} \) \(\mathstrut+\) \(144q^{7} \) \(\mathstrut+\) \(81q^{9} \) \(\mathstrut+O(q^{10}) \)
24.6.1.c 1 \(\Q\) \(q \) \(\mathstrut+\) \(9q^{3} \) \(\mathstrut+\) \(38q^{5} \) \(\mathstrut+\) \(120q^{7} \) \(\mathstrut+\) \(81q^{9} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{6}^{\mathrm{old}}(24) \) into lower level spaces

\( S_{6}^{\mathrm{old}}(24) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/8/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(8)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/6/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(6)) }^{\oplus 3 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/4/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(4)) }^{\oplus 4 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/3/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(3)) }^{\oplus 4 } $