Base field 3.3.1765.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 11x + 16\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, 3w^{2} + 2w - 29]$ |
| Dimension: | $22$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{22} - 8x^{21} + 2x^{20} + 138x^{19} - 277x^{18} - 842x^{17} + 2808x^{16} + 1814x^{15} - 12795x^{14} + 2260x^{13} + 31311x^{12} - 18510x^{11} - 42734x^{10} + 36270x^{9} + 31928x^{8} - 33428x^{7} - 12195x^{6} + 15446x^{5} + 1794x^{4} - 3312x^{3} + 94x^{2} + 240x - 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} - w + 9]$ | $...$ |
| 5 | $[5, 5, -2w^{2} - w + 21]$ | $...$ |
| 5 | $[5, 5, w - 1]$ | $...$ |
| 13 | $[13, 13, -2w^{2} - w + 19]$ | $...$ |
| 13 | $[13, 13, w^{2} - 9]$ | $...$ |
| 13 | $[13, 13, 3w^{2} + 2w - 29]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{2} - 2w + 7]$ | $...$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $...$ |
| 27 | $[27, 3, -3]$ | $...$ |
| 31 | $[31, 31, -w^{2} + 7]$ | $...$ |
| 43 | $[43, 43, w^{2} - 13]$ | $...$ |
| 47 | $[47, 47, 2w^{2} + 3w - 11]$ | $...$ |
| 59 | $[59, 59, w^{2} - 5]$ | $...$ |
| 61 | $[61, 61, 5w^{2} + 4w - 47]$ | $...$ |
| 61 | $[61, 61, 4w - 7]$ | $...$ |
| 61 | $[61, 61, w - 5]$ | $...$ |
| 71 | $[71, 71, -2w^{2} - 2w + 21]$ | $...$ |
| 73 | $[73, 73, -2w^{2} + 4w - 1]$ | $...$ |
| 79 | $[79, 79, w + 5]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, 3w^{2} + 2w - 29]$ | $-1$ |