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: | $[8, 4, -22w + 204]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} - 7x^{17} - 26x^{16} + 246x^{15} + 217x^{14} - 3506x^{13} - 378x^{12} + 26343x^{11} - 3351x^{10} - 113916x^{9} + 15868x^{8} + 290520x^{7} - 13228x^{6} - 429988x^{5} - 42172x^{4} + 341888x^{3} + 88896x^{2} - 113424x - 47312\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -11w + 102]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w - 9]$ | $...$ |
| 5 | $[5, 5, w + 9]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 4w - 37]$ | $...$ |
| 7 | $[7, 7, 4w + 37]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 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 |
|---|---|---|
| $2$ | $[2, 2, -11w + 102]$ | $1$ |