Base field 3.3.1765.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 11x + 16\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| 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:
| \(x^{5} - 3x^{4} - 15x^{3} + 36x^{2} + 48x - 72\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 2]$ | $-1$ |
| 4 | $[4, 2, -w^{2} - w + 9]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -2w^{2} - w + 21]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 1]$ | $-\frac{1}{12}e^{4} + \frac{1}{4}e^{3} + \frac{5}{4}e^{2} - 2e - 3$ |
| 13 | $[13, 13, -2w^{2} - w + 19]$ | $\phantom{-}\frac{1}{12}e^{4} - \frac{1}{4}e^{3} - \frac{5}{4}e^{2} + 2e + 5$ |
| 13 | $[13, 13, w^{2} - 9]$ | $-\frac{1}{12}e^{4} + \frac{1}{4}e^{3} + \frac{1}{4}e^{2} - e + 5$ |
| 13 | $[13, 13, 3w^{2} + 2w - 29]$ | $-e + 2$ |
| 17 | $[17, 17, -w^{2} - 2w + 7]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{2}e^{3} - \frac{9}{2}e^{2} + \frac{7}{2}e + 9$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{1}{6}e^{4} + 3e^{2} + \frac{1}{2}e - 9$ |
| 27 | $[27, 3, -3]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{9}{2}e + 1$ |
| 31 | $[31, 31, -w^{2} + 7]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{13}{2}e - 1$ |
| 43 | $[43, 43, w^{2} - 13]$ | $-\frac{1}{6}e^{4} + \frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 4e + 8$ |
| 47 | $[47, 47, 2w^{2} + 3w - 11]$ | $-\frac{1}{6}e^{4} + \frac{1}{2}e^{3} + \frac{5}{2}e^{2} - 4e - 6$ |
| 59 | $[59, 59, w^{2} - 5]$ | $\phantom{-}\frac{1}{6}e^{4} + \frac{1}{2}e^{3} - \frac{7}{2}e^{2} - 5e + 12$ |
| 61 | $[61, 61, 5w^{2} + 4w - 47]$ | $-\frac{1}{12}e^{4} + \frac{1}{4}e^{3} + \frac{5}{4}e^{2} - 2e - 1$ |
| 61 | $[61, 61, 4w - 7]$ | $-\frac{1}{3}e^{4} + 6e^{2} - 16$ |
| 61 | $[61, 61, w - 5]$ | $\phantom{-}\frac{1}{6}e^{4} + \frac{1}{2}e^{3} - \frac{9}{2}e^{2} - 5e + 20$ |
| 71 | $[71, 71, -2w^{2} - 2w + 21]$ | $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{15}{4}e^{2} + 5e - 9$ |
| 73 | $[73, 73, -2w^{2} + 4w - 1]$ | $\phantom{-}\frac{1}{6}e^{4} - \frac{1}{2}e^{3} - \frac{5}{2}e^{2} + 5e + 8$ |
| 79 | $[79, 79, w + 5]$ | $-2e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 2]$ | $1$ |
| $4$ | $[4, 2, -w^{2} - w + 9]$ | $-1$ |