Base field \(\Q(\sqrt{107}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 107\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 4, -6w + 62]$ |
| Dimension: | $22$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{22} + 2x^{21} - 78x^{20} - 162x^{19} + 2410x^{18} + 5214x^{17} - 37720x^{16} - 84258x^{15} + 318081x^{14} + 717320x^{13} - 1445606x^{12} - 3118404x^{11} + 3599828x^{10} + 6408800x^{9} - 5507276x^{8} - 5707232x^{7} + 4558328x^{6} + 1367456x^{5} - 957008x^{4} - 169024x^{3} + 45248x^{2} + 4352x - 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -3w + 31]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -w - 10]$ | $...$ |
| 7 | $[7, 7, -w + 10]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 13 | $[13, 13, -2w - 21]$ | $...$ |
| 13 | $[13, 13, 2w - 21]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 29 | $[29, 29, -5w + 52]$ | $...$ |
| 29 | $[29, 29, 5w + 52]$ | $...$ |
| 31 | $[31, 31, 4w - 41]$ | $...$ |
| 31 | $[31, 31, 35w - 362]$ | $...$ |
| 37 | $[37, 37, -w - 12]$ | $...$ |
| 37 | $[37, 37, w - 12]$ | $...$ |
| 41 | $[41, 41, -8w + 83]$ | $...$ |
| 41 | $[41, 41, 23w - 238]$ | $...$ |
| 43 | $[43, 43, -w - 8]$ | $...$ |
| 43 | $[43, 43, w - 8]$ | $...$ |
| 53 | $[53, 53, -14w + 145]$ | $...$ |
| 53 | $[53, 53, 17w - 176]$ | $...$ |
| 59 | $[59, 59, 7w - 72]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -3w + 31]$ | $-1$ |