Base field \(\Q(\sqrt{86}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 86\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $44$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $104$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{44} - 90x^{42} + 3775x^{40} - 97988x^{38} + 1762659x^{36} - 23318226x^{34} + 234941497x^{32} - 1842163400x^{30} + 11388679448x^{28} - 55904606848x^{26} + 218393449860x^{24} - 677711552144x^{22} + 1660946378160x^{20} - 3183657898496x^{18} + 4706047415360x^{16} - 5265466467072x^{14} + 4355493665024x^{12} - 2588519737344x^{10} + 1067799165952x^{8} - 291950866432x^{6} + 49185427456x^{4} - 4443406336x^{2} + 151519232\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -11w + 102]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 9]$ | $...$ |
| 5 | $[5, 5, w + 9]$ | $...$ |
| 7 | $[7, 7, 4w - 37]$ | $...$ |
| 7 | $[7, 7, 4w + 37]$ | $...$ |
| 9 | $[9, 3, 3]$ | $-1$ |
| 11 | $[11, 11, 7w + 65]$ | $...$ |
| 11 | $[11, 11, -7w + 65]$ | $...$ |
| 17 | $[17, 17, -2w - 19]$ | $...$ |
| 17 | $[17, 17, 2w - 19]$ | $...$ |
| 29 | $[29, 29, -15w + 139]$ | $...$ |
| 29 | $[29, 29, -15w - 139]$ | $...$ |
| 37 | $[37, 37, -w - 7]$ | $...$ |
| 37 | $[37, 37, w - 7]$ | $...$ |
| 41 | $[41, 41, -40w + 371]$ | $...$ |
| 41 | $[41, 41, 62w - 575]$ | $...$ |
| 43 | $[43, 43, -51w + 473]$ | $...$ |
| 59 | $[59, 59, -5w + 47]$ | $...$ |
| 59 | $[59, 59, 5w + 47]$ | $...$ |
| 61 | $[61, 61, -w - 5]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, 3]$ | $1$ |