Base field 3.3.1944.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 6\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - x^{4} - 12x^{3} + 3x^{2} + 33x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 2w + 2]$ | $-1$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w^{2} - w - 9]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} - w - 7]$ | $\phantom{-}e^{2} - e - 4$ |
| 11 | $[11, 11, w^{2} - w - 1]$ | $-\frac{1}{2}e^{4} + e^{3} + 4e^{2} - \frac{9}{2}e - 6$ |
| 13 | $[13, 13, -2w - 1]$ | $\phantom{-}e^{2} - e - 4$ |
| 17 | $[17, 17, -2w^{2} + 6w + 5]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - 4e^{2} + \frac{9}{2}e + 6$ |
| 31 | $[31, 31, -2w^{2} + 2w + 19]$ | $-e^{4} + 2e^{3} + 9e^{2} - 10e - 16$ |
| 37 | $[37, 37, 2w^{2} - 13]$ | $-e^{3} + 2e^{2} + 5e - 10$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-e^{3} + e^{2} + 6e$ |
| 43 | $[43, 43, 2w^{2} - 2w - 17]$ | $-\frac{1}{2}e^{4} + 2e^{3} + 4e^{2} - \frac{23}{2}e - 10$ |
| 43 | $[43, 43, -2w + 7]$ | $\phantom{-}e^{2} - 4e - 4$ |
| 43 | $[43, 43, 12w^{2} - 8w - 101]$ | $-e^{3} + 2e^{2} + 5e - 4$ |
| 49 | $[49, 7, w^{2} + w - 1]$ | $-\frac{1}{2}e^{4} + 6e^{2} + \frac{1}{2}e - 10$ |
| 59 | $[59, 59, -w^{2} + w + 11]$ | $-\frac{1}{2}e^{4} + 5e^{2} + \frac{3}{2}e - 6$ |
| 61 | $[61, 61, -w^{2} - w - 1]$ | $\phantom{-}8$ |
| 79 | $[79, 79, -2w^{2} + 4w + 7]$ | $\phantom{-}e^{3} - 7e - 4$ |
| 83 | $[83, 83, 2w - 1]$ | $\phantom{-}e^{4} - e^{3} - 9e^{2} + 3e + 12$ |
| 89 | $[89, 89, 5w^{2} - 3w - 43]$ | $-2e^{3} + 2e^{2} + 15e - 6$ |
| 103 | $[103, 103, -2w + 5]$ | $-3e^{2} + 3e + 20$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w^{2} + 2w + 2]$ | $1$ |
| $2$ | $[2, 2, w + 1]$ | $-1$ |