Base field 3.3.697.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} + w + 3]$ |
| 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:
| \(x^{5} - 4x^{4} - 6x^{3} + 34x^{2} - 23x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e$ |
| 11 | $[11, 11, -w^{2} + 2w + 4]$ | $-e^{3} + e^{2} + 9e - 6$ |
| 11 | $[11, 11, -w + 2]$ | $-e + 2$ |
| 11 | $[11, 11, w - 1]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + \frac{9}{2}e^{2} - \frac{25}{2}e + 1$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-e + 4$ |
| 17 | $[17, 17, -w^{2} + w + 8]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + \frac{7}{2}e^{2} - \frac{23}{2}e + 5$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}1$ |
| 19 | $[19, 19, -w^{2} + 6]$ | $-e^{4} + 3e^{3} + 8e^{2} - 26e + 8$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{5}{2}e^{3} - \frac{7}{2}e^{2} + \frac{45}{2}e - 5$ |
| 25 | $[25, 5, w^{2} - 7]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{9}{2}e^{3} - \frac{23}{2}e^{2} + \frac{75}{2}e - 13$ |
| 27 | $[27, 3, -3]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + \frac{9}{2}e^{2} - \frac{25}{2}e + 1$ |
| 31 | $[31, 31, w^{2} - 2w - 8]$ | $-e^{2} + 4$ |
| 37 | $[37, 37, w^{2} - 2w - 6]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{11}{2}e^{2} + \frac{5}{2}e + 9$ |
| 41 | $[41, 41, -w - 4]$ | $-e^{4} + 4e^{3} + 6e^{2} - 34e + 14$ |
| 41 | $[41, 41, w^{2} - 2w - 7]$ | $\phantom{-}e^{4} - 4e^{3} - 7e^{2} + 32e - 10$ |
| 47 | $[47, 47, 2w^{2} - 3w - 7]$ | $\phantom{-}e^{4} - e^{3} - 10e^{2} + 6e + 12$ |
| 53 | $[53, 53, -w^{2} + w + 9]$ | $\phantom{-}e^{2} + e - 4$ |
| 61 | $[61, 61, 3w^{2} - 2w - 17]$ | $-\frac{1}{2}e^{4} + \frac{5}{2}e^{3} + \frac{5}{2}e^{2} - \frac{39}{2}e + 13$ |
| 67 | $[67, 67, 2w - 1]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + \frac{9}{2}e^{2} - \frac{11}{2}e + 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} + w + 3]$ | $-1$ |