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:
| \(x^{5} - x^{4} - 5x^{3} + 3x^{2} + 4x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $-e^{4} + 5e^{2} + e - 3$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e^{3} - e^{2} - 3e + 1$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}e^{4} - e^{3} - 5e^{2} + 3e + 2$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w + 1]$ | $\phantom{-}2e^{4} - 2e^{3} - 9e^{2} + 3e + 5$ |
| 11 | $[11, 11, w + 10]$ | $-e^{4} + 2e^{3} + 4e^{2} - 7e - 3$ |
| 17 | $[17, 17, -3w + 17]$ | $\phantom{-}e^{4} - e^{3} - 4e^{2} + e$ |
| 29 | $[29, 29, w + 11]$ | $-2e^{4} + 2e^{3} + 9e^{2} - 5e - 7$ |
| 29 | $[29, 29, w + 18]$ | $-e^{4} + 3e^{3} + 3e^{2} - 9e - 3$ |
| 37 | $[37, 37, w + 16]$ | $\phantom{-}e^{4} - 2e^{3} - 3e^{2} + 5e - 4$ |
| 37 | $[37, 37, w + 21]$ | $\phantom{-}e^{3} + 3e^{2} - 5e - 11$ |
| 47 | $[47, 47, -w - 9]$ | $\phantom{-}e^{4} - 3e^{3} - 2e^{2} + 9e$ |
| 47 | $[47, 47, w - 9]$ | $\phantom{-}2e^{4} + e^{3} - 13e^{2} - 3e + 11$ |
| 49 | $[49, 7, -7]$ | $-e^{4} - e^{3} + 6e^{2} + e - 3$ |
| 61 | $[61, 61, w + 20]$ | $-4e^{4} + e^{3} + 20e^{2} + 5e - 16$ |
| 61 | $[61, 61, w + 41]$ | $\phantom{-}3e^{4} - e^{3} - 17e^{2} + 2e + 10$ |
| 89 | $[89, 89, 2w - 15]$ | $-e^{4} + 2e^{3} + 3e^{2} - 6e + 4$ |
| 89 | $[89, 89, -2w - 15]$ | $\phantom{-}2e^{4} - 4e^{3} - 10e^{2} + 7e + 14$ |
| 103 | $[103, 103, -14w + 81]$ | $-e^{4} - 3e^{3} + 6e^{2} + 13e - 9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,-w + 2]$ | $-1$ |