Base field 4.4.16225.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 13 x^2 + 6 x + 36\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9,3,-\frac{1}{3} w^3 - \frac{2}{3} w^2 + \frac{7}{3} w + 5]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{3} w^3 - \frac{4}{3} w^2 - \frac{4}{3} w + 6]$ | $-e$ |
| 4 | $[4, 2, -\frac{1}{3} w^3 - \frac{2}{3} w^2 + \frac{10}{3} w + 7]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -\frac{1}{2} w^3 + \frac{3}{2} w^2 + \frac{7}{2} w - 9]$ | $-2$ |
| 9 | $[9, 3, \frac{1}{3} w^3 + \frac{2}{3} w^2 - \frac{7}{3} w - 5]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -\frac{1}{6} w^3 + \frac{1}{6} w^2 + \frac{1}{6} w]$ | $\phantom{-}2 e$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}2 e$ |
| 19 | $[19, 19, \frac{1}{6} w^3 - \frac{1}{6} w^2 - \frac{13}{6} w + 2]$ | $\phantom{-}0$ |
| 25 | $[25, 5, -\frac{1}{3} w^3 + \frac{1}{3} w^2 + \frac{7}{3} w - 1]$ | $-8$ |
| 29 | $[29, 29, -\frac{1}{6} w^3 + \frac{1}{6} w^2 + \frac{13}{6} w]$ | $\phantom{-}0$ |
| 29 | $[29, 29, w - 1]$ | $\phantom{-}0$ |
| 31 | $[31, 31, \frac{1}{3} w^3 - \frac{1}{3} w^2 - \frac{10}{3} w + 3]$ | $-2 e$ |
| 31 | $[31, 31, \frac{1}{6} w^3 - \frac{1}{6} w^2 - \frac{1}{6} w + 2]$ | $-2 e$ |
| 41 | $[41, 41, -\frac{1}{2} w^3 - \frac{1}{2} w^2 + \frac{9}{2} w + 5]$ | $-6 e$ |
| 41 | $[41, 41, -\frac{1}{2} w^3 + \frac{3}{2} w^2 + \frac{5}{2} w - 8]$ | $-4 e$ |
| 59 | $[59, 59, \frac{1}{3} w^3 - \frac{1}{3} w^2 - \frac{10}{3} w - 1]$ | $\phantom{-}0$ |
| 59 | $[59, 59, -\frac{1}{3} w^3 + \frac{4}{3} w^2 + \frac{7}{3} w - 7]$ | $\phantom{-}6$ |
| 59 | $[59, 59, \frac{1}{2} w^3 - \frac{1}{2} w^2 - \frac{5}{2} w + 2]$ | $\phantom{-}0$ |
| 79 | $[79, 79, w^2 - 11]$ | $\phantom{-}10$ |
| 79 | $[79, 79, \frac{1}{6} w^3 - \frac{7}{6} w^2 - \frac{7}{6} w + 3]$ | $-8$ |
| 89 | $[89, 89, -\frac{1}{6} w^3 + \frac{1}{6} w^2 + \frac{19}{6} w - 5]$ | $\phantom{-}2 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9,3,-\frac{1}{3} w^3 - \frac{2}{3} w^2 + \frac{7}{3} w + 5]$ | $-1$ |