Base field \(\Q(\sqrt{185}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 46\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8,4,-2w + 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 3x^{3} - 5x^{2} - 16x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-1$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{9}{2}e - 4$ |
| 11 | $[11, 11, 2w + 13]$ | $\phantom{-}e^{3} + 2e^{2} - 8e - 8$ |
| 11 | $[11, 11, -2w + 15]$ | $-2e^{3} - 4e^{2} + 13e + 16$ |
| 13 | $[13, 13, w + 4]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{5}{2}e + 2$ |
| 13 | $[13, 13, w + 8]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{11}{2}e + 2$ |
| 17 | $[17, 17, w + 3]$ | $\phantom{-}\frac{3}{2}e^{3} + \frac{7}{2}e^{2} - \frac{17}{2}e - 14$ |
| 17 | $[17, 17, w + 13]$ | $-\frac{3}{2}e^{3} - \frac{5}{2}e^{2} + \frac{19}{2}e + 10$ |
| 23 | $[23, 23, w]$ | $-e^{2} + 6$ |
| 23 | $[23, 23, w + 22]$ | $\phantom{-}3e^{3} + 5e^{2} - 21e - 24$ |
| 37 | $[37, 37, w + 18]$ | $-e^{2} - e$ |
| 41 | $[41, 41, -2w + 13]$ | $\phantom{-}e^{3} - 6e + 4$ |
| 41 | $[41, 41, -2w - 11]$ | $\phantom{-}e^{3} + 3e^{2} - 6e - 8$ |
| 43 | $[43, 43, w + 11]$ | $-e^{3} - 3e^{2} + 6e + 14$ |
| 43 | $[43, 43, w + 31]$ | $-e^{3} + 6e - 4$ |
| 49 | $[49, 7, -7]$ | $-\frac{5}{2}e^{3} - \frac{11}{2}e^{2} + \frac{39}{2}e + 24$ |
| 71 | $[71, 71, -2w + 17]$ | $\phantom{-}5e^{3} + 9e^{2} - 34e - 40$ |
| 71 | $[71, 71, -2w - 15]$ | $-e^{3} + 5e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 1]$ | $-1$ |
| $2$ | $[2,2,-w + 2]$ | $1$ |