Base field 4.4.14336.1
Generator \(w\), with minimal polynomial \(x^{4} - 8x^{2} + 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17,17,w^{2} + w - 5]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 4x^{15} - 12x^{14} + 60x^{13} + 47x^{12} - 354x^{11} - 44x^{10} + 1052x^{9} - 145x^{8} - 1666x^{7} + 405x^{6} + 1358x^{5} - 384x^{4} - 500x^{3} + 144x^{2} + 56x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{3} + w^{2} + 5w - 6]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{3} - w^{2} - 5w + 7]$ | $...$ |
| 7 | $[7, 7, -w - 1]$ | $...$ |
| 7 | $[7, 7, w - 1]$ | $...$ |
| 17 | $[17, 17, w^{2} - w - 5]$ | $...$ |
| 17 | $[17, 17, w^{2} + w - 5]$ | $-1$ |
| 23 | $[23, 23, -w - 3]$ | $...$ |
| 23 | $[23, 23, w - 3]$ | $...$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 4w - 3]$ | $...$ |
| 25 | $[25, 5, -w^{3} - w^{2} + 4w + 3]$ | $...$ |
| 41 | $[41, 41, w^{3} - 4w - 1]$ | $...$ |
| 41 | $[41, 41, -w^{3} + 4w - 1]$ | $...$ |
| 71 | $[71, 71, -w^{3} + 2w^{2} + 4w - 9]$ | $...$ |
| 71 | $[71, 71, w^{3} + 2w^{2} - 4w - 9]$ | $...$ |
| 73 | $[73, 73, w^{3} - w^{2} - 5w + 3]$ | $...$ |
| 73 | $[73, 73, w^{3} + w^{2} - 5w - 3]$ | $...$ |
| 79 | $[79, 79, 2w^{2} - 2w - 9]$ | $...$ |
| 79 | $[79, 79, -2w^{3} + 8w + 5]$ | $...$ |
| 81 | $[81, 3, -3]$ | $...$ |
| 89 | $[89, 89, -w^{3} - 2w^{2} + 6w + 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17,17,w^{2} + w - 5]$ | $1$ |