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: | $4$ |
| 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:
| \(x^{4} - 2x^{3} - 10x^{2} + 11x + 29\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $-e + 1$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 5 | $[5, 5, w + 1]$ | $-e^{3} + 2e^{2} + 5e - 5$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}e^{3} - e^{2} - 6e + 1$ |
| 11 | $[11, 11, w + 1]$ | $-e^{2} + e + 7$ |
| 11 | $[11, 11, w + 9]$ | $-e^{2} + e + 7$ |
| 17 | $[17, 17, w + 2]$ | $\phantom{-}e^{3} + 2e^{2} - 8e - 17$ |
| 17 | $[17, 17, w + 14]$ | $-e^{3} + 5e^{2} + e - 22$ |
| 19 | $[19, 19, w]$ | $\phantom{-}e^{3} - 8e - 1$ |
| 19 | $[19, 19, w + 18]$ | $-e^{3} + 3e^{2} + 5e - 8$ |
| 37 | $[37, 37, -w - 4]$ | $\phantom{-}e^{3} - 6e^{2} - 3e + 28$ |
| 37 | $[37, 37, w - 5]$ | $-e^{3} - 3e^{2} + 12e + 20$ |
| 43 | $[43, 43, w + 16]$ | $\phantom{-}3e^{2} - 2e - 19$ |
| 43 | $[43, 43, w + 26]$ | $\phantom{-}3e^{2} - 4e - 18$ |
| 49 | $[49, 7, -7]$ | $-4e^{2} + 4e + 17$ |
| 53 | $[53, 53, -w - 10]$ | $\phantom{-}e^{3} - 3e^{2} - e + 15$ |
| 53 | $[53, 53, w - 11]$ | $-e^{3} + 4e + 12$ |
| 61 | $[61, 61, w + 15]$ | $\phantom{-}e^{3} - 8e^{2} + 4e + 40$ |
| 61 | $[61, 61, w + 45]$ | $-e^{3} - 5e^{2} + 9e + 37$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |