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: | $[7, 7, -2w + 15]$ |
| Dimension: | $22$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $98$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{22} - 33x^{20} + 465x^{18} - 3657x^{16} + 17609x^{14} - 53582x^{12} + 102676x^{10} - 119814x^{8} + 79424x^{6} - 26289x^{4} + 3273x^{2} - 121\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $...$ |
| 3 | $[3, 3, w + 2]$ | $...$ |
| 7 | $[7, 7, -2w + 15]$ | $-1$ |
| 7 | $[7, 7, -2w - 15]$ | $...$ |
| 11 | $[11, 11, w + 5]$ | $...$ |
| 11 | $[11, 11, w + 6]$ | $...$ |
| 19 | $[19, 19, w + 1]$ | $...$ |
| 19 | $[19, 19, w + 18]$ | $...$ |
| 23 | $[23, 23, w + 9]$ | $...$ |
| 23 | $[23, 23, -w + 9]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 29 | $[29, 29, w]$ | $...$ |
| 37 | $[37, 37, w + 13]$ | $...$ |
| 37 | $[37, 37, w + 24]$ | $...$ |
| 43 | $[43, 43, w + 12]$ | $...$ |
| 43 | $[43, 43, w + 31]$ | $...$ |
| 61 | $[61, 61, w + 27]$ | $...$ |
| 61 | $[61, 61, w + 34]$ | $...$ |
| 71 | $[71, 71, 12w - 91]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -2w + 15]$ | $1$ |