Related objects

Learn more about

Show commands for: Magma / SageMath

Decomposition of \( S_{8}^{\mathrm{new}}(10) \) into irreducible Hecke orbits

magma: S := CuspForms(10,8);
magma: N := Newforms(S);
sage: N = Newforms(10,8,names="a")
Label Dimension Field $q$-expansion of eigenform
10.8.1.a 1 \(\Q\) \(q \) \(\mathstrut+\) \(8q^{2} \) \(\mathstrut+\) \(28q^{3} \) \(\mathstrut+\) \(64q^{4} \) \(\mathstrut+\) \(125q^{5} \) \(\mathstrut+\) \(224q^{6} \) \(\mathstrut+\) \(104q^{7} \) \(\mathstrut+\) \(512q^{8} \) \(\mathstrut-\) \(1403q^{9} \) \(\mathstrut+O(q^{10}) \)

Decomposition of \( S_{8}^{\mathrm{old}}(10) \) into lower level spaces

\( S_{8}^{\mathrm{old}}(10) \) \(\cong\) $ \href{ /ModularForm/GL2/Q/holomorphic/5/8/1/ }{ S^{ new }_{ 8 }(\Gamma_0(5)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/2/8/1/ }{ S^{ new }_{ 8 }(\Gamma_0(2)) }^{\oplus 2 } $