# Related objects

Show commands for: Magma / SageMath

## Decomposition of $S_{12}^{\mathrm{new}}(20)$ into irreducible Hecke orbits

magma: S := CuspForms(20,12);
magma: N := Newforms(S);
sage: N = Newforms(20,12,names="a")
Label Dimension Field $q$-expansion of eigenform
20.12.1.a 1 $\Q$ $q$ $\mathstrut+$ $306q^{3}$ $\mathstrut-$ $3125q^{5}$ $\mathstrut-$ $32074q^{7}$ $\mathstrut-$ $83511q^{9}$ $\mathstrut+O(q^{10})$
20.12.1.b 2 $\Q(\alpha_{ 2 })$ $q$ $\mathstrut+$ $\alpha_{2} q^{3}$ $\mathstrut+$ $3125q^{5}$ $\mathstrut+$ $\bigl(111 \alpha_{2}$ $\mathstrut- 10540\bigr)q^{7}$ $\mathstrut+$ $\bigl(220 \alpha_{2}$ $\mathstrut- 2331\bigr)q^{9}$ $\mathstrut+O(q^{10})$

The coefficient fields are:

Coefficient field Minimal polynomial of $\alpha_j$ over $\Q$
$\Q(\alpha_{ 2 })$ $x ^{2}$ $\mathstrut -\mathstrut 220 x$ $\mathstrut -\mathstrut 174816$

## Decomposition of $S_{12}^{\mathrm{old}}(20)$ into lower level spaces

$S_{12}^{\mathrm{old}}(20)$ $\cong$ $\href{ /ModularForm/GL2/Q/holomorphic/10/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(10)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/5/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(5)) }^{\oplus 3 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/4/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(4)) }^{\oplus 2 }\oplus \href{ /ModularForm/GL2/Q/holomorphic/1/12/1/ }{ S^{ new }_{ 12 }(\Gamma_0(1)) }^{\oplus 6 }$