Base field 3.3.785.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, w + 3]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-2$ |
| 5 | $[5, 5, -w + 3]$ | $-e - 1$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}4e + 3$ |
| 9 | $[9, 3, w^{2} + w - 4]$ | $\phantom{-}2e + 4$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $-e - 2$ |
| 23 | $[23, 23, w^{2} - 2]$ | $\phantom{-}5e + 2$ |
| 23 | $[23, 23, w^{2} - 3]$ | $\phantom{-}5e + 1$ |
| 23 | $[23, 23, -w^{2} + 8]$ | $-4e + 2$ |
| 29 | $[29, 29, w - 4]$ | $\phantom{-}2$ |
| 37 | $[37, 37, w^{2} + w - 8]$ | $-4e$ |
| 41 | $[41, 41, w^{2} + 2w - 4]$ | $-4e - 8$ |
| 47 | $[47, 47, 2w^{2} + w - 8]$ | $\phantom{-}4e + 8$ |
| 59 | $[59, 59, -2w^{2} - 3w + 6]$ | $\phantom{-}8e + 6$ |
| 61 | $[61, 61, -2w - 1]$ | $\phantom{-}2e - 4$ |
| 67 | $[67, 67, -2w - 3]$ | $-4e$ |
| 79 | $[79, 79, 2w^{2} - 9]$ | $\phantom{-}3e + 14$ |
| 109 | $[109, 109, w^{2} + 2w - 6]$ | $-4$ |
| 109 | $[109, 109, 2w^{2} + w - 14]$ | $-7e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w + 3]$ | $-1$ |