Base field \(\Q(\sqrt{2}, \sqrt{17})\)
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 11x^{2} + 12x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9,3,-\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{7}{3}]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, \frac{4}{9}w^{3} - \frac{2}{3}w^{2} - \frac{47}{9}w + \frac{20}{9}]$ | $\phantom{-}e$ |
| 2 | $[2, 2, \frac{5}{9}w^{3} - \frac{4}{3}w^{2} - \frac{52}{9}w + \frac{79}{9}]$ | $\phantom{-}e$ |
| 9 | $[9, 3, \frac{1}{3}w^{3} - \frac{11}{3}w - \frac{1}{3}]$ | $-3e - 1$ |
| 9 | $[9, 3, w^{3} - w^{2} - 12w - 1]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -\frac{1}{9}w^{3} - \frac{1}{3}w^{2} + \frac{14}{9}w + \frac{49}{9}]$ | $-2e + 3$ |
| 17 | $[17, 17, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} + \frac{5}{9}w - \frac{59}{9}]$ | $-2e + 3$ |
| 25 | $[25, 5, -\frac{7}{9}w^{3} + \frac{2}{3}w^{2} + \frac{89}{9}w + \frac{19}{9}]$ | $-3e + 3$ |
| 25 | $[25, 5, -\frac{5}{9}w^{3} + \frac{1}{3}w^{2} + \frac{52}{9}w + \frac{11}{9}]$ | $\phantom{-}8e - 5$ |
| 47 | $[47, 47, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} + \frac{5}{9}w - \frac{41}{9}]$ | $\phantom{-}e - 5$ |
| 47 | $[47, 47, \frac{1}{9}w^{3} + \frac{1}{3}w^{2} - \frac{14}{9}w - \frac{13}{9}]$ | $\phantom{-}4e + 6$ |
| 47 | $[47, 47, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} + \frac{5}{9}w - \frac{23}{9}]$ | $\phantom{-}4e + 6$ |
| 47 | $[47, 47, \frac{1}{9}w^{3} + \frac{1}{3}w^{2} - \frac{14}{9}w - \frac{31}{9}]$ | $\phantom{-}e - 5$ |
| 49 | $[49, 7, -\frac{4}{9}w^{3} + \frac{2}{3}w^{2} + \frac{38}{9}w - \frac{29}{9}]$ | $\phantom{-}3e - 9$ |
| 49 | $[49, 7, \frac{4}{9}w^{3} - \frac{2}{3}w^{2} - \frac{38}{9}w + \frac{11}{9}]$ | $\phantom{-}3e - 9$ |
| 89 | $[89, 89, \frac{20}{9}w^{3} - \frac{16}{3}w^{2} - \frac{208}{9}w + \frac{325}{9}]$ | $\phantom{-}4e - 12$ |
| 89 | $[89, 89, \frac{2}{3}w^{3} - w^{2} - \frac{25}{3}w + \frac{7}{3}]$ | $-4e + 7$ |
| 89 | $[89, 89, -\frac{2}{3}w^{3} + w^{2} + \frac{25}{3}w - \frac{19}{3}]$ | $-4e + 7$ |
| 89 | $[89, 89, -2w^{3} + 3w^{2} + 23w - 11]$ | $\phantom{-}4e - 12$ |
| 103 | $[103, 103, \frac{8}{9}w^{3} - \frac{4}{3}w^{2} - \frac{94}{9}w + \frac{67}{9}]$ | $-8e - 5$ |
| 103 | $[103, 103, -\frac{38}{9}w^{3} + \frac{28}{3}w^{2} + \frac{406}{9}w - \frac{541}{9}]$ | $-5e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9,3,-\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{7}{3}]$ | $-1$ |