Base field 4.4.18625.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 14 x^2 + 9 x + 41\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, -\frac{1}{6} w^3 + \frac{7}{3} w + \frac{11}{6}]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{6} w^3 - \frac{7}{3} w - \frac{17}{6}]$ | $\phantom{-}1$ |
| 4 | $[4, 2, w - 3]$ | $-2$ |
| 5 | $[5, 5, -\frac{1}{6} w^3 + w^2 + \frac{1}{3} w - \frac{25}{6}]$ | $\phantom{-}e$ |
| 9 | $[9, 3, \frac{1}{6} w^3 - \frac{7}{3} w + \frac{13}{6}]$ | $-e - 1$ |
| 9 | $[9, 3, -w - 2]$ | $\phantom{-}2$ |
| 11 | $[11, 11, -\frac{1}{6} w^3 + \frac{7}{3} w + \frac{11}{6}]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w + 2]$ | $\phantom{-}0$ |
| 41 | $[41, 41, -w]$ | $-2 e - 6$ |
| 41 | $[41, 41, \frac{1}{6} w^3 - \frac{7}{3} w + \frac{1}{6}]$ | $\phantom{-}4 e$ |
| 59 | $[59, 59, -\frac{1}{6} w^3 + \frac{1}{3} w + \frac{23}{6}]$ | $-3 e + 6$ |
| 59 | $[59, 59, -\frac{1}{3} w^3 + \frac{11}{3} w + \frac{11}{3}]$ | $-2 e$ |
| 61 | $[61, 61, -\frac{5}{3} w^3 - 3 w^2 + \frac{46}{3} w + \frac{79}{3}]$ | $-10$ |
| 61 | $[61, 61, \frac{5}{6} w^3 + w^2 - \frac{23}{3} w - \frac{55}{6}]$ | $\phantom{-}2 e + 8$ |
| 61 | $[61, 61, w^3 + 2 w^2 - 9 w - 17]$ | $-4 e + 2$ |
| 61 | $[61, 61, -\frac{1}{6} w^3 + \frac{10}{3} w + \frac{35}{6}]$ | $-5 e + 2$ |
| 71 | $[71, 71, -\frac{1}{2} w^3 + 2 w^2 + 4 w - \frac{33}{2}]$ | $-4 e + 6$ |
| 71 | $[71, 71, \frac{1}{6} w^3 - w^2 - \frac{4}{3} w + \frac{67}{6}]$ | $\phantom{-}6 e - 6$ |
| 79 | $[79, 79, \frac{1}{2} w^3 - 3 w + \frac{1}{2}]$ | $\phantom{-}10$ |
| 79 | $[79, 79, -\frac{2}{3} w^3 + \frac{19}{3} w - \frac{2}{3}]$ | $\phantom{-}7 e - 5$ |
| 89 | $[89, 89, \frac{1}{2} w^3 + w^2 - 5 w - \frac{15}{2}]$ | $-7 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -\frac{1}{6} w^3 + \frac{7}{3} w + \frac{11}{6}]$ | $-1$ |