Base field 3.3.1229.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 6\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, -2w^{2} - 3w + 5]$ |
| Dimension: | $15$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{15} - 5x^{14} - 10x^{13} + 80x^{12} - 2x^{11} - 460x^{10} + 280x^{9} + 1195x^{8} - 954x^{7} - 1440x^{6} + 1105x^{5} + 762x^{4} - 433x^{3} - 165x^{2} + 43x + 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2} + 2w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 3]$ | $...$ |
| 4 | $[4, 2, -w^{2} + w + 5]$ | $...$ |
| 9 | $[9, 3, w^{2} + 2w - 1]$ | $...$ |
| 11 | $[11, 11, w + 1]$ | $...$ |
| 13 | $[13, 13, -2w^{2} - 3w + 5]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -2w + 5]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $...$ |
| 23 | $[23, 23, -w^{2} + 2w + 1]$ | $...$ |
| 29 | $[29, 29, 3w^{2} + 6w - 5]$ | $...$ |
| 37 | $[37, 37, 4w^{2} - 2w - 25]$ | $...$ |
| 67 | $[67, 67, 2w^{2} + 2w - 7]$ | $...$ |
| 67 | $[67, 67, -2w^{2} - 5w + 1]$ | $...$ |
| 67 | $[67, 67, 2w^{2} + 3w - 7]$ | $...$ |
| 71 | $[71, 71, w - 5]$ | $...$ |
| 73 | $[73, 73, w^{2} + 2w - 5]$ | $...$ |
| 73 | $[73, 73, 2w^{2} - w - 11]$ | $...$ |
| 73 | $[73, 73, -2w - 1]$ | $...$ |
| 83 | $[83, 83, 4w^{2} - 31]$ | $...$ |
| 97 | $[97, 97, 2w^{2} + 2w - 5]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -2w^{2} - 3w + 5]$ | $-1$ |