Base field \(\Q(\sqrt{34}) \)
Generator \(w\), with minimal polynomial \(x^2 - 34\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5,5,-w + 2]$ |
| Dimension: | $5$ |
| 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:
| \(x^5 - x^4 - 5 x^3 + 3 x^2 + 4 x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e^4 - 5 e^2 - e + 3$ |
| 3 | $[3, 3, w + 2]$ | $-e^3 + e^2 + 3 e - 1$ |
| 5 | $[5, 5, w + 2]$ | $-e^4 + e^3 + 5 e^2 - 3 e - 2$ |
| 5 | $[5, 5, w + 3]$ | $-1$ |
| 11 | $[11, 11, w + 1]$ | $-2 e^4 + 2 e^3 + 9 e^2 - 3 e - 5$ |
| 11 | $[11, 11, w + 10]$ | $\phantom{-}e^4 - 2 e^3 - 4 e^2 + 7 e + 3$ |
| 17 | $[17, 17, -3 w + 17]$ | $\phantom{-}e^4 - e^3 - 4 e^2 + e$ |
| 29 | $[29, 29, w + 11]$ | $\phantom{-}2 e^4 - 2 e^3 - 9 e^2 + 5 e + 7$ |
| 29 | $[29, 29, w + 18]$ | $\phantom{-}e^4 - 3 e^3 - 3 e^2 + 9 e + 3$ |
| 37 | $[37, 37, w + 16]$ | $-e^4 + 2 e^3 + 3 e^2 - 5 e + 4$ |
| 37 | $[37, 37, w + 21]$ | $-e^3 - 3 e^2 + 5 e + 11$ |
| 47 | $[47, 47, -w - 9]$ | $\phantom{-}e^4 - 3 e^3 - 2 e^2 + 9 e$ |
| 47 | $[47, 47, w - 9]$ | $\phantom{-}2 e^4 + e^3 - 13 e^2 - 3 e + 11$ |
| 49 | $[49, 7, -7]$ | $-e^4 - e^3 + 6 e^2 + e - 3$ |
| 61 | $[61, 61, w + 20]$ | $\phantom{-}4 e^4 - e^3 - 20 e^2 - 5 e + 16$ |
| 61 | $[61, 61, w + 41]$ | $-3 e^4 + e^3 + 17 e^2 - 2 e - 10$ |
| 89 | $[89, 89, 2 w - 15]$ | $-e^4 + 2 e^3 + 3 e^2 - 6 e + 4$ |
| 89 | $[89, 89, -2 w - 15]$ | $\phantom{-}2 e^4 - 4 e^3 - 10 e^2 + 7 e + 14$ |
| 103 | $[103, 103, -14 w + 81]$ | $-e^4 - 3 e^3 + 6 e^2 + 13 e - 9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,-w + 2]$ | $1$ |