Base field \(\Q(\sqrt{58}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 58\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 4x^{3} - 8x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 1]$ | $-e - 2$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -2w + 15]$ | $\phantom{-}e^{3} + 2e^{2} - 3e - 2$ |
| 7 | $[7, 7, -2w - 15]$ | $-e^{3} - 4e^{2} - e + 4$ |
| 11 | $[11, 11, w + 5]$ | $-e^{3} - 4e^{2} - 2e + 4$ |
| 11 | $[11, 11, w + 6]$ | $\phantom{-}e^{3} + 2e^{2} - 2e$ |
| 19 | $[19, 19, w + 1]$ | $-e^{3} - 2e^{2} + 3e + 2$ |
| 19 | $[19, 19, w + 18]$ | $\phantom{-}e^{3} + 4e^{2} + e - 4$ |
| 23 | $[23, 23, w + 9]$ | $-e^{3} - 2e^{2} + 3e - 2$ |
| 23 | $[23, 23, -w + 9]$ | $\phantom{-}e^{3} + 4e^{2} + e - 8$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}2e^{2} + 4e - 5$ |
| 29 | $[29, 29, w]$ | $\phantom{-}2e^{2} + 4e + 2$ |
| 37 | $[37, 37, w + 13]$ | $-2e^{2} + 12$ |
| 37 | $[37, 37, w + 24]$ | $-2e^{2} - 8e + 4$ |
| 43 | $[43, 43, w + 12]$ | $\phantom{-}e^{3} + 6e^{2} + 6e - 4$ |
| 43 | $[43, 43, w + 31]$ | $-e^{3} + 6e$ |
| 61 | $[61, 61, w + 27]$ | $-2e^{3} - 5e^{2} + 2e - 3$ |
| 61 | $[61, 61, w + 34]$ | $\phantom{-}2e^{3} + 7e^{2} + 2e - 11$ |
| 71 | $[71, 71, 12w - 91]$ | $-2e^{2} - 2e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |