# Related objects

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

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