Base field 3.3.1300.1
Generator \(w\), with minimal polynomial \(x^{3} - 10x - 10\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 4x^{4} - 9x^{3} + 38x^{2} + 18x - 76\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -w^{2} + 2w + 5]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 3]$ | $-e^{2} + e + 6$ |
| 11 | $[11, 11, -2w^{2} + 5w + 9]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 3e + 8$ |
| 13 | $[13, 13, -w^{2} + w + 7]$ | $-\frac{1}{4}e^{4} + \frac{3}{4}e^{3} + 2e^{2} - \frac{9}{2}e - 5$ |
| 13 | $[13, 13, w - 3]$ | $-e^{2} + 2e + 6$ |
| 17 | $[17, 17, -w^{2} + 2w + 7]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{4}e^{3} - \frac{5}{2}e^{2} + \frac{1}{2}e + 3$ |
| 17 | $[17, 17, -2w^{2} + 5w + 7]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - \frac{11}{2}e^{2} + 6e + 12$ |
| 17 | $[17, 17, -w^{2} + 3w + 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 2e + 8$ |
| 19 | $[19, 19, -w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - 2e + 14$ |
| 27 | $[27, 3, -3]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 7e^{2} - 3e - 18$ |
| 31 | $[31, 31, w^{2} - 2w - 9]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 6e^{2} - 2e - 16$ |
| 37 | $[37, 37, w^{2} - 7]$ | $-\frac{3}{4}e^{4} + \frac{5}{4}e^{3} + 10e^{2} - \frac{17}{2}e - 25$ |
| 41 | $[41, 41, w^{2} - w - 11]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{4}e^{3} - \frac{3}{2}e^{2} - \frac{1}{2}e - 3$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 10$ |
| 49 | $[49, 7, w^{2} - 3w - 1]$ | $-\frac{1}{4}e^{4} + \frac{7}{4}e^{3} - e^{2} - \frac{21}{2}e + 7$ |
| 59 | $[59, 59, w^{2} - 4w + 1]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 7e^{2} + e - 26$ |
| 67 | $[67, 67, w^{2} - 3w - 7]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{11}{2}e^{2} - 6e - 14$ |
| 71 | $[71, 71, 4w + 9]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 8e^{2} - 28$ |
| 73 | $[73, 73, -4w^{2} + 8w + 23]$ | $-\frac{1}{4}e^{4} + \frac{5}{4}e^{3} + \frac{3}{2}e^{2} - \frac{17}{2}e + 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 2]$ | $-1$ |