Base field 3.3.1300.1
Generator \(w\), with minimal polynomial \(x^{3} - 10x - 10\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, -w^{2} + w + 7]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 3x^{13} - 15x^{12} + 47x^{11} + 77x^{10} - 255x^{9} - 175x^{8} + 596x^{7} + 202x^{6} - 589x^{5} - 152x^{4} + 216x^{3} + 56x^{2} - 22x - 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{2} + 2w + 5]$ | $...$ |
| 7 | $[7, 7, w + 3]$ | $...$ |
| 11 | $[11, 11, -2w^{2} + 5w + 9]$ | $...$ |
| 13 | $[13, 13, -w^{2} + w + 7]$ | $\phantom{-}1$ |
| 13 | $[13, 13, w - 3]$ | $...$ |
| 17 | $[17, 17, -w^{2} + 2w + 7]$ | $...$ |
| 17 | $[17, 17, -2w^{2} + 5w + 7]$ | $...$ |
| 17 | $[17, 17, -w^{2} + 3w + 3]$ | $...$ |
| 19 | $[19, 19, -w + 1]$ | $...$ |
| 27 | $[27, 3, -3]$ | $...$ |
| 31 | $[31, 31, w^{2} - 2w - 9]$ | $...$ |
| 37 | $[37, 37, w^{2} - 7]$ | $...$ |
| 41 | $[41, 41, w^{2} - w - 11]$ | $...$ |
| 47 | $[47, 47, w^{2} - 3]$ | $...$ |
| 49 | $[49, 7, w^{2} - 3w - 1]$ | $...$ |
| 59 | $[59, 59, w^{2} - 4w + 1]$ | $...$ |
| 67 | $[67, 67, w^{2} - 3w - 7]$ | $...$ |
| 71 | $[71, 71, 4w + 9]$ | $...$ |
| 73 | $[73, 73, -4w^{2} + 8w + 23]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w^{2} + w + 7]$ | $-1$ |