Base field \(\Q(\sqrt{2}, \sqrt{17})\)
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 11 x^2 + 12 x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 4, \frac{2}{9} w^3 - \frac{1}{3} w^2 - \frac{28}{9} w + \frac{10}{9}]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, \frac{4}{9} w^3 - \frac{2}{3} w^2 - \frac{47}{9} w + \frac{20}{9}]$ | $\phantom{-}0$ |
| 2 | $[2, 2, \frac{5}{9} w^3 - \frac{4}{3} w^2 - \frac{52}{9} w + \frac{79}{9}]$ | $\phantom{-}0$ |
| 9 | $[9, 3, \frac{1}{3} w^3 - \frac{11}{3} w - \frac{1}{3}]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^3 - w^2 - 12 w - 1]$ | $-e$ |
| 17 | $[17, 17, -\frac{1}{9} w^3 - \frac{1}{3} w^2 + \frac{14}{9} w + \frac{49}{9}]$ | $\phantom{-}2 e$ |
| 17 | $[17, 17, -\frac{1}{9} w^3 + \frac{2}{3} w^2 + \frac{5}{9} w - \frac{59}{9}]$ | $-2 e$ |
| 25 | $[25, 5, -\frac{7}{9} w^3 + \frac{2}{3} w^2 + \frac{89}{9} w + \frac{19}{9}]$ | $-2 e$ |
| 25 | $[25, 5, -\frac{5}{9} w^3 + \frac{1}{3} w^2 + \frac{52}{9} w + \frac{11}{9}]$ | $\phantom{-}2 e$ |
| 47 | $[47, 47, -\frac{1}{9} w^3 + \frac{2}{3} w^2 + \frac{5}{9} w - \frac{41}{9}]$ | $-10$ |
| 47 | $[47, 47, \frac{1}{9} w^3 + \frac{1}{3} w^2 - \frac{14}{9} w - \frac{13}{9}]$ | $-8$ |
| 47 | $[47, 47, -\frac{1}{9} w^3 + \frac{2}{3} w^2 + \frac{5}{9} w - \frac{23}{9}]$ | $-10$ |
| 47 | $[47, 47, \frac{1}{9} w^3 + \frac{1}{3} w^2 - \frac{14}{9} w - \frac{31}{9}]$ | $-8$ |
| 49 | $[49, 7, -\frac{4}{9} w^3 + \frac{2}{3} w^2 + \frac{38}{9} w - \frac{29}{9}]$ | $\phantom{-}8$ |
| 49 | $[49, 7, \frac{4}{9} w^3 - \frac{2}{3} w^2 - \frac{38}{9} w + \frac{11}{9}]$ | $\phantom{-}8$ |
| 89 | $[89, 89, \frac{20}{9} w^3 - \frac{16}{3} w^2 - \frac{208}{9} w + \frac{325}{9}]$ | $\phantom{-}0$ |
| 89 | $[89, 89, \frac{2}{3} w^3 - w^2 - \frac{25}{3} w + \frac{7}{3}]$ | $\phantom{-}8$ |
| 89 | $[89, 89, -\frac{2}{3} w^3 + w^2 + \frac{25}{3} w - \frac{19}{3}]$ | $\phantom{-}0$ |
| 89 | $[89, 89, -2 w^3 + 3 w^2 + 23 w - 11]$ | $\phantom{-}8$ |
| 103 | $[103, 103, \frac{8}{9} w^3 - \frac{4}{3} w^2 - \frac{94}{9} w + \frac{67}{9}]$ | $-4 e$ |
| 103 | $[103, 103, -\frac{38}{9} w^3 + \frac{28}{3} w^2 + \frac{406}{9} w - \frac{541}{9}]$ | $\phantom{-}4 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, \frac{4}{9} w^3 - \frac{2}{3} w^2 - \frac{47}{9} w + \frac{20}{9}]$ | $-1$ |