Base field \(\Q(\sqrt{145}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 36\); narrow class number \(4\) and class number \(4\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5, 5, w + 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $84$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 4x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-e$ |
| 3 | $[3, 3, w]$ | $-e^{3} + 3e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e^{3} - 3e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w + 1]$ | $-3e^{3} + 13e$ |
| 17 | $[17, 17, w + 15]$ | $\phantom{-}3e^{3} - 13e$ |
| 29 | $[29, 29, w + 14]$ | $-6e^{2} + 12$ |
| 37 | $[37, 37, w + 10]$ | $-3e^{3} + 9e$ |
| 37 | $[37, 37, w + 26]$ | $\phantom{-}3e^{3} - 9e$ |
| 43 | $[43, 43, w + 19]$ | $\phantom{-}3e^{3} - 9e$ |
| 43 | $[43, 43, w + 23]$ | $-3e^{3} + 9e$ |
| 47 | $[47, 47, w + 22]$ | $\phantom{-}3e^{3} - 17e$ |
| 47 | $[47, 47, w + 24]$ | $-3e^{3} + 17e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}2e^{2} - 14$ |
| 59 | $[59, 59, w + 16]$ | $-6$ |
| 59 | $[59, 59, w + 42]$ | $-6$ |
| 71 | $[71, 71, w + 21]$ | $-6$ |
| 71 | $[71, 71, w + 49]$ | $-6$ |
| 73 | $[73, 73, w + 13]$ | $-3e^{3} + 3e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w + 2]$ | $-1$ |