Decomposition of \( S_{12}^{\mathrm{new}}(24) \) into irreducible Hecke orbits
magma: S := CuspForms(24,12);
magma: N := Newforms(S);
magma: N := Newforms(S);
sage: N = Newforms(24,12,names="a")
Label | Dimension | Field | $q$-expansion of eigenform |
---|---|---|---|
24.12.1.a | 1 | \(\Q\) | \(q \) \(\mathstrut-\) \(243q^{3} \) \(\mathstrut-\) \(7130q^{5} \) \(\mathstrut-\) \(19536q^{7} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \) |
24.12.1.b | 1 | \(\Q\) | \(q \) \(\mathstrut-\) \(243q^{3} \) \(\mathstrut+\) \(1190q^{5} \) \(\mathstrut+\) \(18480q^{7} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \) |
24.12.1.c | 1 | \(\Q\) | \(q \) \(\mathstrut+\) \(243q^{3} \) \(\mathstrut+\) \(1870q^{5} \) \(\mathstrut-\) \(72312q^{7} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \) |
24.12.1.d | 2 | $\Q(\alpha_{ 4 })$ | \(q \) \(\mathstrut+\) \(243q^{3} \) \(\mathstrut+\) \(\bigl(\frac{1}{2} \alpha_{4} \) \(\mathstrut+ 243\bigr)q^{5} \) \(\mathstrut+\) \(\bigl(- \frac{1}{2} \alpha_{4} \) \(\mathstrut+ 19427\bigr)q^{7} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \) |
The coefficient fields are:
Coefficient field | Minimal polynomial of $\alpha_j$ over $\Q$ |
---|---|
$\Q(\alpha_{ 4 })\cong$ \(\Q(\sqrt{3061}) \) | \(x ^{2} \) \(\mathstrut -\mathstrut 2156 x \) \(\mathstrut -\mathstrut 450200732\) |