Base field 4.4.17609.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[8, 8, -w^{3} + 6w - 3]$ |
| 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:
| \(x^{5} - 19x^{3} + 10x^{2} + 56x - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w^{3} + w^{2} - 4w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{3} + 6w - 2]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 5$ |
| 8 | $[8, 2, w^{3} - 7w + 3]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{5}{2}e - 1$ |
| 11 | $[11, 11, -w^{3} + 6w - 4]$ | $-2$ |
| 17 | $[17, 17, w^{3} + w^{2} - 6w - 1]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{17}{4}e^{2} + 2e + 7$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{7}{2}e^{2} - 4$ |
| 31 | $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ | $-2e - 2$ |
| 37 | $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{3}{4}e^{3} - \frac{7}{2}e^{2} - \frac{11}{2}e + 7$ |
| 41 | $[41, 41, w^{2} + 2w - 4]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{4}e^{3} - 4e^{2} - \frac{1}{2}e + 5$ |
| 47 | $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{17}{4}e^{2} + e + 9$ |
| 47 | $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e - 1$ |
| 59 | $[59, 59, -2w^{3} + 13w - 6]$ | $-\frac{1}{2}e^{2} + \frac{3}{2}e + 5$ |
| 59 | $[59, 59, -w^{3} - w^{2} + 5w + 2]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 8e^{2} - e - 14$ |
| 59 | $[59, 59, w^{2} + w - 1]$ | $\phantom{-}e^{2} + 3e - 10$ |
| 59 | $[59, 59, w^{2} + 2w - 6]$ | $-\frac{1}{4}e^{4} + \frac{1}{2}e^{3} + \frac{19}{4}e^{2} - 8e - 11$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 8w - 7]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{3}{4}e^{3} - 4e^{2} - 8e + 10$ |
| 67 | $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ | $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + 6e + 8$ |
| 73 | $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{19}{2}e + 1$ |
| 81 | $[81, 3, -3]$ | $-\frac{1}{4}e^{4} + \frac{1}{2}e^{3} + \frac{19}{4}e^{2} - 9e - 9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 1]$ | $-1$ |