Base field 3.3.1849.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 14x - 8\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8,8,w^{2} - 2w - 11]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + x^{4} - 5x^{3} - 4x^{2} + 4x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ | $\phantom{-}e$ |
| 2 | $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ | $-e^{2} + 2$ |
| 2 | $[2, 2, w + 3]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -w^{2} + 3w + 7]$ | $\phantom{-}e^{3} - 3e$ |
| 11 | $[11, 11, -2w - 1]$ | $\phantom{-}2e^{4} + e^{3} - 9e^{2} - 5e + 5$ |
| 11 | $[11, 11, -w^{2} + w + 11]$ | $-e^{4} - e^{3} + 5e^{2} + 5e - 4$ |
| 27 | $[27, 3, 3]$ | $-2e^{3} + 2e^{2} + 8e - 2$ |
| 41 | $[41, 41, 2w + 5]$ | $-3e^{4} - 3e^{3} + 14e^{2} + 7e - 9$ |
| 41 | $[41, 41, -w^{2} + 3w + 3]$ | $\phantom{-}3e^{4} + e^{3} - 16e^{2} - 7e + 11$ |
| 41 | $[41, 41, -w^{2} + w + 15]$ | $-e^{4} - e^{3} + 4e^{2} + 5e - 3$ |
| 43 | $[43, 43, -3w^{2} + 11w + 11]$ | $-2e^{4} + 10e^{2} - 2e - 8$ |
| 47 | $[47, 47, -w^{2} - w + 5]$ | $-e^{4} + 3e^{3} + 2e^{2} - 11e + 5$ |
| 47 | $[47, 47, w^{2} - 5w - 3]$ | $-e^{4} - e^{3} + 2e^{2} + 5e - 1$ |
| 47 | $[47, 47, -2w^{2} + 4w + 23]$ | $-5e^{4} - 3e^{3} + 22e^{2} + 11e - 11$ |
| 59 | $[59, 59, -w^{2} + w + 13]$ | $\phantom{-}e^{4} - 2e^{2} - 9$ |
| 59 | $[59, 59, w^{2} - 3w - 5]$ | $\phantom{-}3e^{4} - 2e^{3} - 11e^{2} + 4e - 4$ |
| 59 | $[59, 59, -2w - 3]$ | $-4e^{4} - 4e^{3} + 17e^{2} + 10e - 9$ |
| 97 | $[97, 97, 7w^{2} - 11w - 91]$ | $\phantom{-}e^{4} - e^{3} - 4e^{2} + e + 3$ |
| 97 | $[97, 97, -2w^{2} - 8w - 5]$ | $-5e^{4} - e^{3} + 24e^{2} + 5e - 19$ |
| 97 | $[97, 97, 5w^{2} - 19w - 15]$ | $-3e^{4} + e^{3} + 14e^{2} - 3e - 9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,w + 3]$ | $1$ |