Base field 3.3.1708.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, -w^{2} + w + 9]$ |
| Dimension: | $17$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $31$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{17} - 26x^{15} + x^{14} + 269x^{13} - 18x^{12} - 1412x^{11} + 123x^{10} + 3981x^{9} - 407x^{8} - 5921x^{7} + 689x^{6} + 4346x^{5} - 586x^{4} - 1332x^{3} + 200x^{2} + 88x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w^{2} - 2w - 5]$ | $...$ |
| 5 | $[5, 5, w^{2} + 3w + 1]$ | $...$ |
| 7 | $[7, 7, -2w^{2} + 2w + 17]$ | $...$ |
| 7 | $[7, 7, -w^{2} + w + 9]$ | $\phantom{-}1$ |
| 13 | $[13, 13, 2w + 1]$ | $...$ |
| 25 | $[25, 5, -3w^{2} + 5w + 19]$ | $...$ |
| 27 | $[27, 3, 3]$ | $...$ |
| 29 | $[29, 29, w^{2} + w - 1]$ | $...$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $...$ |
| 37 | $[37, 37, 2w^{2} + 6w + 3]$ | $...$ |
| 41 | $[41, 41, -6w^{2} - 14w - 3]$ | $...$ |
| 53 | $[53, 53, -4w^{2} + 6w + 27]$ | $...$ |
| 59 | $[59, 59, 2w^{2} - 4w - 11]$ | $...$ |
| 61 | $[61, 61, w^{2} - w - 3]$ | $...$ |
| 61 | $[61, 61, -2w^{2} + 2w + 13]$ | $...$ |
| 73 | $[73, 73, w^{2} + 3w + 3]$ | $...$ |
| 97 | $[97, 97, w^{2} + w - 15]$ | $...$ |
| 101 | $[101, 101, w^{2} + 3w - 1]$ | $...$ |
| 101 | $[101, 101, w^{2} - w - 11]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w^{2} + w + 9]$ | $-1$ |