Base field 3.3.961.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 8\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 8, -w^{2} + 9]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - x^{4} - 7x^{3} + 5x^{2} + 10x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, \frac{1}{2}w^{2} - \frac{1}{2}w - 4]$ | $\phantom{-}e$ |
| 2 | $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 3]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{5}{2}e^{2} + \frac{3}{2}e + 2$ |
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}0$ |
| 23 | $[23, 23, -w^{2} + w + 7]$ | $\phantom{-}e^{4} - e^{3} - 7e^{2} + 5e + 6$ |
| 23 | $[23, 23, w^{2} + w - 7]$ | $\phantom{-}e^{3} + e^{2} - 5e - 1$ |
| 23 | $[23, 23, -2w + 1]$ | $\phantom{-}e^{4} - 6e^{2} + 5$ |
| 27 | $[27, 3, 3]$ | $-2e^{3} + e^{2} + 10e - 1$ |
| 29 | $[29, 29, -w^{2} - 3w + 1]$ | $-e^{4} + e^{3} + 6e^{2} - e - 7$ |
| 29 | $[29, 29, w^{2} - 3w + 1]$ | $\phantom{-}2e^{3} - e^{2} - 8e + 5$ |
| 29 | $[29, 29, -2w^{2} + 21]$ | $-e^{3} + 2e^{2} + 3e - 6$ |
| 31 | $[31, 31, -3w^{2} + w + 31]$ | $-e^{3} - 2e^{2} + 5e + 6$ |
| 47 | $[47, 47, 2w - 3]$ | $-e^{3} - 3e^{2} + 5e + 11$ |
| 47 | $[47, 47, w^{2} + w - 5]$ | $\phantom{-}e^{4} - 3e^{3} - 3e^{2} + 11e - 2$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $\phantom{-}e^{3} - e^{2} - e + 5$ |
| 61 | $[61, 61, w^{2} - w - 11]$ | $\phantom{-}e^{3} - 2e^{2} - 5e + 4$ |
| 61 | $[61, 61, -w^{2} - w + 3]$ | $\phantom{-}3e^{4} - 2e^{3} - 17e^{2} + 8e + 14$ |
| 61 | $[61, 61, -2w + 5]$ | $-e^{4} - e^{3} + 6e^{2} + 3e - 1$ |
| 89 | $[89, 89, w^{2} - w - 1]$ | $-3e^{3} + 4e^{2} + 13e - 12$ |
| 89 | $[89, 89, w^{2} + w - 13]$ | $-e^{4} - e^{3} + 8e^{2} + 5e - 17$ |
| 89 | $[89, 89, -2w - 5]$ | $\phantom{-}e^{4} - 9e^{2} - 6e + 16$ |
Atkin-Lehner eigenvalues
The Atkin-Lehner eigenvalues for this form are not in the database.