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

magma: S := CuspForms(8,8);
magma: N := Newforms(S);
sage: N = Newforms(8,8,names="a")
Label Dimension Field $q$-expansion of eigenform
8.8.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(84q^{3} \) \(\mathstrut-\) \(82q^{5} \) \(\mathstrut-\) \(456q^{7} \) \(\mathstrut+\) \(4869q^{9} \) \(\mathstrut+O(q^{10}) \)
8.8.1.b 1 \(\Q\) \(q \) \(\mathstrut+\) \(44q^{3} \) \(\mathstrut+\) \(430q^{5} \) \(\mathstrut-\) \(1224q^{7} \) \(\mathstrut-\) \(251q^{9} \) \(\mathstrut+O(q^{10}) \)

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

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