# Related objects

Show commands for: Magma / SageMath

## Decomposition of $S_{10}^{\mathrm{new}}(6)$ into irreducible Hecke orbits

magma: S := CuspForms(6,10);
magma: N := Newforms(S);
sage: N = Newforms(6,10,names="a")
Label Dimension Field $q$-expansion of eigenform
6.10.1.a 1 $\Q$ $q$ $\mathstrut-$ $16q^{2}$ $\mathstrut+$ $81q^{3}$ $\mathstrut+$ $256q^{4}$ $\mathstrut+$ $2694q^{5}$ $\mathstrut-$ $1296q^{6}$ $\mathstrut-$ $3544q^{7}$ $\mathstrut-$ $4096q^{8}$ $\mathstrut+$ $6561q^{9}$ $\mathstrut+O(q^{10})$

## Decomposition of $S_{10}^{\mathrm{old}}(6)$ into lower level spaces

$S_{10}^{\mathrm{old}}(6)$ $\cong$ $\href{ /ModularForm/GL2/Q/holomorphic/3/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(3)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/2/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(2)) }^{\oplus 2 }$