Base field 3.3.148.1
Generator \(w\), with minimal polynomial \(x^3 - x^2 - 3 x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[29, 29, w^2 - 3 w - 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^2 + w + 1]$ | $\phantom{-}2 e$ |
| 13 | $[13, 13, -w^2 + 2 w + 2]$ | $\phantom{-}0$ |
| 17 | $[17, 17, 2 w + 1]$ | $-2 e - 4$ |
| 19 | $[19, 19, -w^2 + 2 w + 4]$ | $-2 e - 2$ |
| 23 | $[23, 23, -w^2 - w + 3]$ | $-2 e + 2$ |
| 25 | $[25, 5, -2 w^2 + w + 4]$ | $-2 e + 4$ |
| 27 | $[27, 3, 3]$ | $-2 e + 6$ |
| 29 | $[29, 29, w^2 - 3 w - 1]$ | $\phantom{-}1$ |
| 31 | $[31, 31, 2 w^2 - 2 w - 3]$ | $\phantom{-}4$ |
| 37 | $[37, 37, w^2 + w - 5]$ | $\phantom{-}4 e - 2$ |
| 37 | $[37, 37, w - 4]$ | $-4$ |
| 43 | $[43, 43, 2 w^2 - w - 2]$ | $\phantom{-}4 e + 4$ |
| 59 | $[59, 59, 2 w^2 - 3 w - 6]$ | $\phantom{-}2 e - 2$ |
| 61 | $[61, 61, -3 w^2 + 4 w + 4]$ | $-8 e + 2$ |
| 67 | $[67, 67, -w - 4]$ | $-6 e + 2$ |
| 67 | $[67, 67, -3 w^2 + 8]$ | $-2 e - 10$ |
| 67 | $[67, 67, w^2 - 3 w - 3]$ | $-4 e - 4$ |
| 79 | $[79, 79, w^2 + 2 w - 4]$ | $-2 e + 2$ |
| 89 | $[89, 89, 3 w^2 - 3 w - 5]$ | $-12 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, w^2 - 3 w - 1]$ | $-1$ |