Base field 4.4.17069.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} - 4x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, w^{3} - w^{2} - 8w - 5]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + 2x^{2} - 2x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-e - 1$ |
| 3 | $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ | $-e^{2} - 2e + 1$ |
| 16 | $[16, 2, 2]$ | $-e^{2} - 2e + 3$ |
| 17 | $[17, 17, w^{3} - w^{2} - 8w - 5]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ | $\phantom{-}e^{2} + 2e - 3$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}3$ |
| 17 | $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ | $-2e^{2} - e + 5$ |
| 25 | $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ | $-3e^{2} - 3e + 6$ |
| 25 | $[25, 5, w^{2} - 2w - 7]$ | $-2e^{2} - 5e + 1$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ | $\phantom{-}2e^{2} + 2e$ |
| 29 | $[29, 29, w - 2]$ | $\phantom{-}3e^{2} + 2e - 9$ |
| 53 | $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ | $-2e^{2} + e + 2$ |
| 53 | $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ | $\phantom{-}2e^{2} + 2e - 11$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ | $\phantom{-}5e^{2} + 7e - 12$ |
| 61 | $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ | $-2e^{2} - 6e + 2$ |
| 101 | $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ | $\phantom{-}6e^{2} + 7e - 12$ |
| 103 | $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ | $\phantom{-}6e^{2} + 11e - 10$ |
| 103 | $[103, 103, -w^{3} + w^{2} + 8w + 2]$ | $\phantom{-}4e - 2$ |
| 113 | $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ | $\phantom{-}2e + 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{3} - w^{2} - 8w - 5]$ | $-1$ |