Base field \(\Q(\sqrt{449}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 112\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5,5,116w - 1287]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $101$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 10]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w - 11]$ | $-2e - 1$ |
| 5 | $[5, 5, -116w - 1171]$ | $-2e - 2$ |
| 5 | $[5, 5, 116w - 1287]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -1002w - 10115]$ | $\phantom{-}2e + 3$ |
| 7 | $[7, 7, 1002w - 11117]$ | $-2e - 2$ |
| 9 | $[9, 3, 3]$ | $-2e - 4$ |
| 11 | $[11, 11, 10w - 111]$ | $\phantom{-}2e - 3$ |
| 11 | $[11, 11, -10w - 101]$ | $\phantom{-}0$ |
| 23 | $[23, 23, -32w + 355]$ | $-4e - 6$ |
| 23 | $[23, 23, 32w + 323]$ | $-6e - 3$ |
| 41 | $[41, 41, -8w - 81]$ | $\phantom{-}2e + 8$ |
| 41 | $[41, 41, -8w + 89]$ | $-2e - 8$ |
| 53 | $[53, 53, 4w - 45]$ | $-6$ |
| 53 | $[53, 53, 4w + 41]$ | $-8e - 5$ |
| 59 | $[59, 59, -3892w + 43181]$ | $\phantom{-}6e + 9$ |
| 59 | $[59, 59, 3892w + 39289]$ | $-2e - 1$ |
| 61 | $[61, 61, 770w - 8543]$ | $\phantom{-}6$ |
| 61 | $[61, 61, -770w - 7773]$ | $\phantom{-}8e + 5$ |
| 67 | $[67, 67, 158w + 1595]$ | $-6e - 9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,116w - 1287]$ | $-1$ |