# Related objects

Show commands for: Magma / SageMath

## Decomposition of $S_{4}^{\mathrm{new}}(11)$ into irreducible Hecke orbits

magma: S := CuspForms(11,4);
magma: N := Newforms(S);
sage: N = Newforms(11,4,names="a")
Label Dimension Field $q$-expansion of eigenform
11.4.1.a 2 $\Q(\alpha_{ 1 })$ $q$ $\mathstrut+$ $\alpha_{1} q^{2}$ $\mathstrut+$ $\bigl(- 4 \alpha_{1}$ $\mathstrut+ 3\bigr)q^{3}$ $\mathstrut+$ $\bigl(2 \alpha_{1}$ $\mathstrut- 6\bigr)q^{4}$ $\mathstrut+$ $\bigl(8 \alpha_{1}$ $\mathstrut- 7\bigr)q^{5}$ $\mathstrut+$ $\bigl(- 5 \alpha_{1}$ $\mathstrut- 8\bigr)q^{6}$ $\mathstrut+$ $\bigl(- 4 \alpha_{1}$ $\mathstrut+ 14\bigr)q^{7}$ $\mathstrut+$ $\bigl(- 10 \alpha_{1}$ $\mathstrut+ 4\bigr)q^{8}$ $\mathstrut+$ $\bigl(8 \alpha_{1}$ $\mathstrut+ 14\bigr)q^{9}$ $\mathstrut+O(q^{10})$

The coefficient fields are:

Coefficient field Minimal polynomial of $\alpha_j$ over $\Q$
$\Q(\alpha_{ 1 })\cong$ $\Q(\sqrt{3})$ $x ^{2}$ $\mathstrut -\mathstrut 2 x$ $\mathstrut -\mathstrut 2$