Base field 4.4.13768.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 2x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w + 3]$ |
| Dimension: | $15$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $33$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{15} - 5x^{14} - 11x^{13} + 87x^{12} + 3x^{11} - 580x^{10} + 406x^{9} + 1830x^{8} - 2012x^{7} - 2671x^{6} + 3809x^{5} + 1359x^{4} - 2752x^{3} + 62x^{2} + 508x - 66\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $...$ |
| 4 | $[4, 2, -w^{2} - w + 1]$ | $...$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $...$ |
| 17 | $[17, 17, -w + 3]$ | $-1$ |
| 27 | $[27, 3, w^{3} - 2w^{2} - 3w + 5]$ | $...$ |
| 31 | $[31, 31, -w^{2} - 2w + 1]$ | $...$ |
| 41 | $[41, 41, -w^{2} + 5]$ | $...$ |
| 43 | $[43, 43, w^{3} - w^{2} - 5w - 1]$ | $...$ |
| 43 | $[43, 43, w^{3} - w^{2} - 3w + 1]$ | $...$ |
| 59 | $[59, 59, -w - 3]$ | $...$ |
| 59 | $[59, 59, -2w^{3} + 2w^{2} + 9w - 5]$ | $...$ |
| 59 | $[59, 59, -w^{3} - 3w^{2} - w + 3]$ | $...$ |
| 59 | $[59, 59, w^{3} - 7w + 1]$ | $...$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 2w + 5]$ | $...$ |
| 61 | $[61, 61, -w^{3} - w^{2} + 4w + 3]$ | $...$ |
| 67 | $[67, 67, 4w^{3} - 4w^{2} - 18w + 7]$ | $...$ |
| 73 | $[73, 73, -2w^{3} + 6w - 3]$ | $...$ |
| 73 | $[73, 73, -2w + 3]$ | $...$ |
| 97 | $[97, 97, w^{3} - 2w^{2} - 5w + 3]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w + 3]$ | $1$ |