# Related objects

Show commands for: Magma / SageMath

## Decomposition of $S_{8}^{\mathrm{new}}(18)$ into irreducible Hecke orbits

magma: S := CuspForms(18,8);
magma: N := Newforms(S);
sage: N = Newforms(18,8,names="a")
Label Dimension Field $q$-expansion of eigenform
18.8.1.a 1 $\Q$ $q$ $\mathstrut-$ $8q^{2}$ $\mathstrut+$ $64q^{4}$ $\mathstrut+$ $114q^{5}$ $\mathstrut-$ $1576q^{7}$ $\mathstrut-$ $512q^{8}$ $\mathstrut+O(q^{10})$
18.8.1.b 1 $\Q$ $q$ $\mathstrut+$ $8q^{2}$ $\mathstrut+$ $64q^{4}$ $\mathstrut+$ $210q^{5}$ $\mathstrut+$ $1016q^{7}$ $\mathstrut+$ $512q^{8}$ $\mathstrut+O(q^{10})$

## Decomposition of $S_{8}^{\mathrm{old}}(18)$ into lower level spaces

$S_{8}^{\mathrm{old}}(18)$ $\cong$ $\href{ /ModularForm/GL2/Q/holomorphic/9/8/1/ }{ S^{ new }_{ 8 }(\Gamma_0(9)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/6/8/1/ }{ S^{ new }_{ 8 }(\Gamma_0(6)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/3/8/1/ }{ S^{ new }_{ 8 }(\Gamma_0(3)) }^{\oplus 4 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/2/8/1/ }{ S^{ new }_{ 8 }(\Gamma_0(2)) }^{\oplus 3 }$