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Decomposition of \( S_{10}^{\mathrm{new}}(6) \) into irreducible Hecke orbits

magma: S := CuspForms(6,10);
magma: N := Newforms(S);
sage: N = Newforms(6,10,names="a")
Label Dimension Field $q$-expansion of eigenform
6.10.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(16q^{2} \) \(\mathstrut+\) \(81q^{3} \) \(\mathstrut+\) \(256q^{4} \) \(\mathstrut+\) \(2694q^{5} \) \(\mathstrut-\) \(1296q^{6} \) \(\mathstrut-\) \(3544q^{7} \) \(\mathstrut-\) \(4096q^{8} \) \(\mathstrut+\) \(6561q^{9} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{10}^{\mathrm{old}}(6) \) into lower level spaces

\( S_{10}^{\mathrm{old}}(6) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/3/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(3)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/2/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(2)) }^{\oplus 2 } $