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

magma: S := CuspForms(10,10);
magma: N := Newforms(S);
sage: N = Newforms(10,10,names="a")
Label Dimension Field $q$-expansion of eigenform
10.10.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(16q^{2} \) \(\mathstrut-\) \(204q^{3} \) \(\mathstrut+\) \(256q^{4} \) \(\mathstrut+\) \(625q^{5} \) \(\mathstrut+\) \(3264q^{6} \) \(\mathstrut+\) \(5432q^{7} \) \(\mathstrut-\) \(4096q^{8} \) \(\mathstrut+\) \(21933q^{9} \) \(\mathstrut+O(q^{10}) \)
10.10.1.b 1 \(\Q\) \(q \) \(\mathstrut-\) \(16q^{2} \) \(\mathstrut+\) \(46q^{3} \) \(\mathstrut+\) \(256q^{4} \) \(\mathstrut-\) \(625q^{5} \) \(\mathstrut-\) \(736q^{6} \) \(\mathstrut-\) \(10318q^{7} \) \(\mathstrut-\) \(4096q^{8} \) \(\mathstrut-\) \(17567q^{9} \) \(\mathstrut+O(q^{10}) \)
10.10.1.c 1 \(\Q\) \(q \) \(\mathstrut+\) \(16q^{2} \) \(\mathstrut+\) \(174q^{3} \) \(\mathstrut+\) \(256q^{4} \) \(\mathstrut-\) \(625q^{5} \) \(\mathstrut+\) \(2784q^{6} \) \(\mathstrut+\) \(4658q^{7} \) \(\mathstrut+\) \(4096q^{8} \) \(\mathstrut+\) \(10593q^{9} \) \(\mathstrut+O(q^{10}) \)

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

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