Related objects

Learn more about

Show commands for: Magma / SageMath

Decomposition of \( S_{2}^{\mathrm{new}}(23) \) into irreducible Hecke orbits

magma: S := CuspForms(23,2);
magma: N := Newforms(S);
sage: N = Newforms(23,2,names="a")
Label Dimension Field $q$-expansion of eigenform
23.2.1.a 2 $\Q(\alpha_{ 1 })$ \(q \) \(\mathstrut+\) \(\alpha_{1} q^{2} \) \(\mathstrut+\) \(\bigl(- 2 \alpha_{1} \) \(\mathstrut- 1\bigr)q^{3} \) \(\mathstrut+\) \(\bigl(- \alpha_{1} \) \(\mathstrut- 1\bigr)q^{4} \) \(\mathstrut+\) \(2 \alpha_{1} q^{5} \) \(\mathstrut+\) \(\bigl(\alpha_{1} \) \(\mathstrut- 2\bigr)q^{6} \) \(\mathstrut+\) \(\bigl(2 \alpha_{1} \) \(\mathstrut+ 2\bigr)q^{7} \) \(\mathstrut+\) \(\bigl(- 2 \alpha_{1} \) \(\mathstrut- 1\bigr)q^{8} \) \(\mathstrut+\) \(2q^{9} \) \(\mathstrut+O(q^{10}) \)

The coefficient fields are:

Coefficient field Minimal polynomial of $\alpha_j$ over $\Q$
$\Q(\alpha_{ 1 })\cong$ \(\Q(\sqrt{5}) \) \(x ^{2} \) \(\mathstrut +\mathstrut x \) \(\mathstrut -\mathstrut 1\)