# Related objects

Show commands for: Magma / SageMath

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

magma: S := CuspForms(10,6);
magma: N := Newforms(S);
sage: N = Newforms(10,6,names="a")
Label Dimension Field $q$-expansion of eigenform
10.6.1.a 1 $\Q$ $q$ $\mathstrut-$ $4q^{2}$ $\mathstrut-$ $26q^{3}$ $\mathstrut+$ $16q^{4}$ $\mathstrut-$ $25q^{5}$ $\mathstrut+$ $104q^{6}$ $\mathstrut-$ $22q^{7}$ $\mathstrut-$ $64q^{8}$ $\mathstrut+$ $433q^{9}$ $\mathstrut+O(q^{10})$
10.6.1.b 1 $\Q$ $q$ $\mathstrut-$ $4q^{2}$ $\mathstrut+$ $24q^{3}$ $\mathstrut+$ $16q^{4}$ $\mathstrut+$ $25q^{5}$ $\mathstrut-$ $96q^{6}$ $\mathstrut-$ $172q^{7}$ $\mathstrut-$ $64q^{8}$ $\mathstrut+$ $333q^{9}$ $\mathstrut+O(q^{10})$
10.6.1.c 1 $\Q$ $q$ $\mathstrut+$ $4q^{2}$ $\mathstrut+$ $6q^{3}$ $\mathstrut+$ $16q^{4}$ $\mathstrut-$ $25q^{5}$ $\mathstrut+$ $24q^{6}$ $\mathstrut-$ $118q^{7}$ $\mathstrut+$ $64q^{8}$ $\mathstrut-$ $207q^{9}$ $\mathstrut+O(q^{10})$

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

$S_{6}^{\mathrm{old}}(10)$ $\cong$ $\href{ /ModularForm/GL2/Q/holomorphic/5/6/1/ }{ S^{ new }_{ 6 }(\Gamma_0(5)) }^{\oplus 2 }$