Base field 4.4.16609.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - x + 9\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[8, 8, -w^{3} + w^{2} + 5w - 5]$ |
| Dimension: | $4$ |
| 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:
| \(x^{4} + 3x^{3} - 8x^{2} - 9x + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + w + 4]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -w^{2} + w + 3]$ | $-\frac{1}{3}e^{3} - e^{2} + \frac{5}{3}e + 1$ |
| 5 | $[5, 5, w^{2} - 4]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{3} - w^{2} - 4w + 5]$ | $\phantom{-}\frac{1}{6}e^{3} - \frac{7}{3}e + \frac{3}{2}$ |
| 17 | $[17, 17, -w^{2} + w + 5]$ | $\phantom{-}\frac{1}{6}e^{3} + e^{2} + \frac{2}{3}e - \frac{9}{2}$ |
| 27 | $[27, 3, -w^{3} + 4w - 2]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{17}{3}e$ |
| 29 | $[29, 29, -w^{2} + w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} + 2e^{2} - e - \frac{19}{2}$ |
| 29 | $[29, 29, -w^{3} + 4w + 2]$ | $-\frac{1}{6}e^{3} + e^{2} + \frac{13}{3}e - \frac{9}{2}$ |
| 37 | $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ | $-\frac{2}{3}e^{3} - 3e^{2} + \frac{10}{3}e + 10$ |
| 41 | $[41, 41, w^{3} - w^{2} - 5w + 2]$ | $\phantom{-}\frac{1}{3}e^{3} + 2e^{2} - \frac{2}{3}e - 8$ |
| 43 | $[43, 43, -w^{3} + w^{2} + 3w - 4]$ | $-\frac{1}{3}e^{3} - 2e^{2} - \frac{7}{3}e + 4$ |
| 61 | $[61, 61, w^{2} - 2w - 2]$ | $\phantom{-}e^{3} + 4e^{2} - 2e - 6$ |
| 61 | $[61, 61, 2w^{2} - w - 8]$ | $-\frac{5}{6}e^{3} - 2e^{2} + \frac{14}{3}e - \frac{5}{2}$ |
| 67 | $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ | $-2e^{2} - 3e + 9$ |
| 73 | $[73, 73, -w^{2} - 2w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} + 2e^{2} - 5e - \frac{15}{2}$ |
| 79 | $[79, 79, w^{2} - 2w - 4]$ | $\phantom{-}\frac{5}{3}e^{3} + 6e^{2} - \frac{28}{3}e - 13$ |
| 89 | $[89, 89, w^{2} + w - 5]$ | $-\frac{3}{2}e^{3} - 5e^{2} + 7e + \frac{7}{2}$ |
| 89 | $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ | $\phantom{-}\frac{7}{6}e^{3} + 2e^{2} - \frac{37}{3}e - \frac{3}{2}$ |
| 89 | $[89, 89, w^{3} - 5w - 5]$ | $-e^{2} - 6e + 4$ |
| 89 | $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ | $-e^{3} - e^{2} + 9e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w^{2} + w + 4]$ | $-1$ |