# Related objects

Show commands for: Magma / SageMath

## Decomposition of $S_{6}^{\mathrm{new}}(11)$ into irreducible Hecke orbits

magma: S := CuspForms(11,6);
magma: N := Newforms(S);
sage: N = Newforms(11,6,names="a")
Label Dimension Field $q$-expansion of eigenform
11.6.1.a 1 $\Q$ $q$ $\mathstrut-$ $4q^{2}$ $\mathstrut-$ $15q^{3}$ $\mathstrut-$ $16q^{4}$ $\mathstrut-$ $19q^{5}$ $\mathstrut+$ $60q^{6}$ $\mathstrut+$ $10q^{7}$ $\mathstrut+$ $192q^{8}$ $\mathstrut-$ $18q^{9}$ $\mathstrut+O(q^{10})$
11.6.1.b 3 $\Q(\alpha_{ 2 })$ $q$ $\mathstrut+$ $\alpha_{2} q^{2}$ $\mathstrut+$ $\bigl(- \frac{1}{6} \alpha_{2} ^{2}$ $\mathstrut- \frac{5}{3} \alpha_{2}$ $\mathstrut+ \frac{64}{3}\bigr)q^{3}$ $\mathstrut+$ $\bigl(\alpha_{2} ^{2}$ $\mathstrut- 32\bigr)q^{4}$ $\mathstrut+$ $\bigl(- \frac{3}{2} \alpha_{2} ^{2}$ $\mathstrut- 7 \alpha_{2}$ $\mathstrut+ 98\bigr)q^{5}$ $\mathstrut+$ $\bigl(- \frac{5}{3} \alpha_{2} ^{2}$ $\mathstrut+ \frac{19}{3} \alpha_{2}$ $\mathstrut+ \frac{94}{3}\bigr)q^{6}$ $\mathstrut+$ $\bigl(5 \alpha_{2} ^{2}$ $\mathstrut+ 10 \alpha_{2}$ $\mathstrut- 272\bigr)q^{7}$ $\mathstrut+$ $\bigl(26 \alpha_{2}$ $\mathstrut- 188\bigr)q^{8}$ $\mathstrut+$ $\bigl(- \frac{11}{6} \alpha_{2} ^{2}$ $\mathstrut- \frac{79}{3} \alpha_{2}$ $\mathstrut+ \frac{323}{3}\bigr)q^{9}$ $\mathstrut+O(q^{10})$

The coefficient fields are:

Coefficient field Minimal polynomial of $\alpha_j$ over $\Q$
$\Q(\alpha_{ 2 })$ $x ^{3}$ $\mathstrut -\mathstrut 90 x$ $\mathstrut +\mathstrut 188$