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

magma: S := CuspForms(10,6);
magma: N := Newforms(S);
sage: N = Newforms(10,6,names="a")
Label Dimension Field $q$-expansion of eigenform
10.6.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(4q^{2} \) \(\mathstrut-\) \(26q^{3} \) \(\mathstrut+\) \(16q^{4} \) \(\mathstrut-\) \(25q^{5} \) \(\mathstrut+\) \(104q^{6} \) \(\mathstrut-\) \(22q^{7} \) \(\mathstrut-\) \(64q^{8} \) \(\mathstrut+\) \(433q^{9} \) \(\mathstrut+O(q^{10}) \)
10.6.1.b 1 \(\Q\) \(q \) \(\mathstrut-\) \(4q^{2} \) \(\mathstrut+\) \(24q^{3} \) \(\mathstrut+\) \(16q^{4} \) \(\mathstrut+\) \(25q^{5} \) \(\mathstrut-\) \(96q^{6} \) \(\mathstrut-\) \(172q^{7} \) \(\mathstrut-\) \(64q^{8} \) \(\mathstrut+\) \(333q^{9} \) \(\mathstrut+O(q^{10}) \)
10.6.1.c 1 \(\Q\) \(q \) \(\mathstrut+\) \(4q^{2} \) \(\mathstrut+\) \(6q^{3} \) \(\mathstrut+\) \(16q^{4} \) \(\mathstrut-\) \(25q^{5} \) \(\mathstrut+\) \(24q^{6} \) \(\mathstrut-\) \(118q^{7} \) \(\mathstrut+\) \(64q^{8} \) \(\mathstrut-\) \(207q^{9} \) \(\mathstrut+O(q^{10}) \)

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

\( S_{6}^{\mathrm{old}}(10) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/5/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(5)) }^{\oplus 2 } $