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: | $[4, 2, 2]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 3x + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{3}e + 1$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e + 3$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{1}{3}e$ |
| 11 | $[11, 11, w + 1]$ | $-e$ |
| 11 | $[11, 11, w + 9]$ | $-\frac{1}{3}e - 1$ |
| 17 | $[17, 17, w + 2]$ | $-e$ |
| 17 | $[17, 17, w + 14]$ | $\phantom{-}e + 3$ |
| 19 | $[19, 19, w]$ | $\phantom{-}e + 3$ |
| 19 | $[19, 19, w + 18]$ | $\phantom{-}\frac{1}{3}e$ |
| 37 | $[37, 37, -w - 4]$ | $-2$ |
| 37 | $[37, 37, w - 5]$ | $-10$ |
| 43 | $[43, 43, w + 16]$ | $\phantom{-}\frac{1}{3}e$ |
| 43 | $[43, 43, w + 26]$ | $\phantom{-}e + 3$ |
| 49 | $[49, 7, -7]$ | $-2$ |
| 53 | $[53, 53, -w - 10]$ | $-10$ |
| 53 | $[53, 53, w - 11]$ | $\phantom{-}6$ |
| 61 | $[61, 61, w + 15]$ | $\phantom{-}\frac{13}{3}e + 13$ |
| 61 | $[61, 61, w + 45]$ | $\phantom{-}5e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $-1$ |