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Decomposition of \( S_{4}^{\mathrm{new}}(22) \) into irreducible Hecke orbits

magma: S := CuspForms(22,4);
magma: N := Newforms(S);
sage: N = Newforms(22,4,names="a")
Label Dimension Field $q$-expansion of eigenform
22.4.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(2q^{2} \) \(\mathstrut-\) \(7q^{3} \) \(\mathstrut+\) \(4q^{4} \) \(\mathstrut-\) \(19q^{5} \) \(\mathstrut+\) \(14q^{6} \) \(\mathstrut+\) \(14q^{7} \) \(\mathstrut-\) \(8q^{8} \) \(\mathstrut+\) \(22q^{9} \) \(\mathstrut+O(q^{10}) \)
22.4.1.b 1 \(\Q\) \(q \) \(\mathstrut-\) \(2q^{2} \) \(\mathstrut+\) \(4q^{3} \) \(\mathstrut+\) \(4q^{4} \) \(\mathstrut+\) \(14q^{5} \) \(\mathstrut-\) \(8q^{6} \) \(\mathstrut-\) \(8q^{7} \) \(\mathstrut-\) \(8q^{8} \) \(\mathstrut-\) \(11q^{9} \) \(\mathstrut+O(q^{10}) \)
22.4.1.c 1 \(\Q\) \(q \) \(\mathstrut+\) \(2q^{2} \) \(\mathstrut+\) \(q^{3} \) \(\mathstrut+\) \(4q^{4} \) \(\mathstrut-\) \(3q^{5} \) \(\mathstrut+\) \(2q^{6} \) \(\mathstrut-\) \(10q^{7} \) \(\mathstrut+\) \(8q^{8} \) \(\mathstrut-\) \(26q^{9} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{4}^{\mathrm{old}}(22) \) into lower level spaces

\( S_{4}^{\mathrm{old}}(22) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/11/4/1/ }{ S^{ new }_{ 4 }(\Gamma_0(11)) }^{\oplus 2 } $