Base field 3.3.1509.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 8, -w^{2} + 8]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 3x^{4} - 4x^{3} + 11x^{2} + 4x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 6]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -2w^{2} + w + 15]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - e^{2} + \frac{5}{2}e - 1$ |
| 4 | $[4, 2, -w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - 2e^{2} + \frac{9}{2}e + 1$ |
| 11 | $[11, 11, w + 3]$ | $-e^{4} + 2e^{3} + 4e^{2} - 3e - 3$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $-\frac{1}{2}e^{4} + \frac{5}{2}e^{3} - 2e^{2} - \frac{13}{2}e + 5$ |
| 23 | $[23, 23, -2w^{2} + 2w + 17]$ | $\phantom{-}2e^{2} - 3e - 3$ |
| 31 | $[31, 31, -w^{2} + 2w + 1]$ | $-e^{4} + e^{3} + 9e^{2} - 3e - 14$ |
| 37 | $[37, 37, 2w^{2} - 13]$ | $-e^{4} + e^{3} + 8e^{2} - 12$ |
| 43 | $[43, 43, 5w^{2} - 2w - 35]$ | $\phantom{-}2e^{4} - 6e^{3} - 3e^{2} + 9e - 4$ |
| 43 | $[43, 43, 3w - 1]$ | $\phantom{-}e^{3} - e^{2} - 6e$ |
| 43 | $[43, 43, 2w - 3]$ | $\phantom{-}e^{3} - 2e^{2} - 2e - 2$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}e^{3} - 3e^{2} - e + 6$ |
| 59 | $[59, 59, -3w^{2} + 2w + 21]$ | $-e^{3} + 2e^{2} + 3e - 6$ |
| 71 | $[71, 71, 2w + 3]$ | $-e^{4} - 2e^{3} + 16e^{2} + 5e - 26$ |
| 71 | $[71, 71, 3w^{2} - 19]$ | $\phantom{-}e^{3} - 3e^{2} - 7e + 10$ |
| 71 | $[71, 71, 4w^{2} - 13w + 5]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - 8e^{2} + \frac{5}{2}e + 15$ |
| 83 | $[83, 83, 2w^{2} - 15]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + 2e^{2} + \frac{7}{2}e - 15$ |
| 89 | $[89, 89, -w^{2} - 1]$ | $\phantom{-}e^{4} - e^{3} - 8e^{2} + 6$ |
| 89 | $[89, 89, 2w^{2} - 4w + 1]$ | $\phantom{-}2e^{4} - 3e^{3} - 12e^{2} + 9e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w^{2} + 6]$ | $1$ |