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Decomposition of \( S_{10}^{\mathrm{new}}(16) \) into irreducible Hecke orbits

magma: S := CuspForms(16,10);
magma: N := Newforms(S);
sage: N = Newforms(16,10,names="a")
Label Dimension Field $q$-expansion of eigenform
16.10.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(228q^{3} \) \(\mathstrut-\) \(666q^{5} \) \(\mathstrut+\) \(6328q^{7} \) \(\mathstrut+\) \(32301q^{9} \) \(\mathstrut+O(q^{10}) \)
16.10.1.b 1 \(\Q\) \(q \) \(\mathstrut-\) \(68q^{3} \) \(\mathstrut+\) \(1510q^{5} \) \(\mathstrut-\) \(10248q^{7} \) \(\mathstrut-\) \(15059q^{9} \) \(\mathstrut+O(q^{10}) \)
16.10.1.c 1 \(\Q\) \(q \) \(\mathstrut+\) \(60q^{3} \) \(\mathstrut-\) \(2074q^{5} \) \(\mathstrut+\) \(4344q^{7} \) \(\mathstrut-\) \(16083q^{9} \) \(\mathstrut+O(q^{10}) \)
16.10.1.d 1 \(\Q\) \(q \) \(\mathstrut+\) \(156q^{3} \) \(\mathstrut+\) \(870q^{5} \) \(\mathstrut+\) \(952q^{7} \) \(\mathstrut+\) \(4653q^{9} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{10}^{\mathrm{old}}(16) \) into lower level spaces

\( S_{10}^{\mathrm{old}}(16) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/8/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(8)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/4/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(4)) }^{\oplus 3 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/2/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(2)) }^{\oplus 4 } $