# Related objects

Show commands for: Magma / SageMath

## Decomposition of $S_{10}^{\mathrm{new}}(18)$ into irreducible Hecke orbits

magma: S := CuspForms(18,10);
magma: N := Newforms(S);
sage: N = Newforms(18,10,names="a")
Label Dimension Field $q$-expansion of eigenform
18.10.1.a 1 $\Q$ $q$ $\mathstrut-$ $16q^{2}$ $\mathstrut+$ $256q^{4}$ $\mathstrut-$ $870q^{5}$ $\mathstrut-$ $952q^{7}$ $\mathstrut-$ $4096q^{8}$ $\mathstrut+O(q^{10})$
18.10.1.b 1 $\Q$ $q$ $\mathstrut-$ $16q^{2}$ $\mathstrut+$ $256q^{4}$ $\mathstrut-$ $384q^{5}$ $\mathstrut+$ $5852q^{7}$ $\mathstrut-$ $4096q^{8}$ $\mathstrut+O(q^{10})$
18.10.1.c 1 $\Q$ $q$ $\mathstrut+$ $16q^{2}$ $\mathstrut+$ $256q^{4}$ $\mathstrut-$ $2694q^{5}$ $\mathstrut-$ $3544q^{7}$ $\mathstrut+$ $4096q^{8}$ $\mathstrut+O(q^{10})$
18.10.1.d 1 $\Q$ $q$ $\mathstrut+$ $16q^{2}$ $\mathstrut+$ $256q^{4}$ $\mathstrut+$ $384q^{5}$ $\mathstrut+$ $5852q^{7}$ $\mathstrut+$ $4096q^{8}$ $\mathstrut+O(q^{10})$

## Decomposition of $S_{10}^{\mathrm{old}}(18)$ into lower level spaces

$S_{10}^{\mathrm{old}}(18)$ $\cong$ $\href{ /ModularForm/GL2/Q/holomorphic/9/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(9)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/6/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(6)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/3/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(3)) }^{\oplus 4 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/2/10/1/ }{ S^{ new }_{ 10 }(\Gamma_0(2)) }^{\oplus 3 }$