Base field \(\Q(\sqrt{229}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9,9,-w + 4]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $99$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + x^{2} - 2x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}0$ |
| 4 | $[4, 2, 2]$ | $-e^{2} - e + 2$ |
| 5 | $[5, 5, w + 1]$ | $-2e^{2} - e + 2$ |
| 5 | $[5, 5, w + 3]$ | $-e^{2} + 1$ |
| 11 | $[11, 11, w + 1]$ | $\phantom{-}2e$ |
| 11 | $[11, 11, w + 9]$ | $\phantom{-}e^{2} + 2e$ |
| 17 | $[17, 17, w + 2]$ | $\phantom{-}3e^{2} - 5$ |
| 17 | $[17, 17, w + 14]$ | $\phantom{-}3e^{2} + e - 5$ |
| 19 | $[19, 19, w]$ | $-3e^{2} + e + 7$ |
| 19 | $[19, 19, w + 18]$ | $\phantom{-}e^{2} + 4e - 4$ |
| 37 | $[37, 37, -w - 4]$ | $-3e^{2} - 3e + 7$ |
| 37 | $[37, 37, w - 5]$ | $\phantom{-}7e^{2} + 2e - 10$ |
| 43 | $[43, 43, w + 16]$ | $\phantom{-}2e^{2} - 2e - 3$ |
| 43 | $[43, 43, w + 26]$ | $-4e^{2} - 3e + 7$ |
| 49 | $[49, 7, -7]$ | $-e - 7$ |
| 53 | $[53, 53, -w - 10]$ | $-8e^{2} - 3e + 14$ |
| 53 | $[53, 53, w - 11]$ | $\phantom{-}3e^{2} - 5e - 7$ |
| 61 | $[61, 61, w + 15]$ | $\phantom{-}4e^{2} + e + 3$ |
| 61 | $[61, 61, w + 45]$ | $\phantom{-}4e - 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 1]$ | $-1$ |