Base field 3.3.1304.1
Generator \(w\), with minimal polynomial \(x^{3} - 11x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 3, w^{2} + w - 7]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 22x^{12} - x^{11} + 186x^{10} + 22x^{9} - 762x^{8} - 156x^{7} + 1566x^{6} + 432x^{5} - 1495x^{4} - 449x^{3} + 526x^{2} + 148x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ | $...$ |
| 3 | $[3, 3, -w^{2} + 3w + 1]$ | $...$ |
| 9 | $[9, 3, w^{2} + w - 7]$ | $\phantom{-}1$ |
| 11 | $[11, 11, 2w^{2} - 21]$ | $...$ |
| 17 | $[17, 17, -\frac{1}{2}w^{2} + \frac{5}{2}w]$ | $...$ |
| 19 | $[19, 19, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ | $...$ |
| 37 | $[37, 37, w^{2} - w - 13]$ | $...$ |
| 37 | $[37, 37, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ | $...$ |
| 37 | $[37, 37, \frac{5}{2}w^{2} - \frac{17}{2}w - 2]$ | $...$ |
| 47 | $[47, 47, -\frac{3}{2}w^{2} + \frac{11}{2}w]$ | $...$ |
| 53 | $[53, 53, w^{2} - w - 7]$ | $...$ |
| 59 | $[59, 59, 2w - 1]$ | $...$ |
| 61 | $[61, 61, -\frac{3}{2}w^{2} + \frac{3}{2}w + 20]$ | $...$ |
| 67 | $[67, 67, w^{2} - 3w - 3]$ | $...$ |
| 71 | $[71, 71, w^{2} - w - 1]$ | $...$ |
| 73 | $[73, 73, 3w^{2} - w - 33]$ | $...$ |
| 79 | $[79, 79, w^{2} - w - 11]$ | $...$ |
| 79 | $[79, 79, w^{2} - 3w + 1]$ | $...$ |
| 79 | $[79, 79, -2w - 5]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, w^{2} + w - 7]$ | $-1$ |