Base field 3.3.564.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, w^{2} - 2w - 2]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + x^{2} - 3x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $\phantom{-}e^{2} - 3$ |
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e^{2} + e - 3$ |
| 13 | $[13, 13, w^{2} - 2w - 2]$ | $-1$ |
| 17 | $[17, 17, -w^{2} + 2]$ | $\phantom{-}e^{2} + 2e - 7$ |
| 19 | $[19, 19, -w^{2} + w + 1]$ | $-e^{2} - 2e + 3$ |
| 31 | $[31, 31, -w + 4]$ | $-e^{2} + 4$ |
| 41 | $[41, 41, -w^{2} + 2w - 2]$ | $-2e^{2} - 2e + 2$ |
| 41 | $[41, 41, -2w^{2} - 3w + 4]$ | $-e^{2} + e + 9$ |
| 41 | $[41, 41, 2w + 1]$ | $-e^{2}$ |
| 43 | $[43, 43, -w^{2} - w + 5]$ | $-e^{2} - 3$ |
| 47 | $[47, 47, -w^{2} + 8]$ | $\phantom{-}e^{2} - 4e - 7$ |
| 47 | $[47, 47, 2w^{2} - w - 8]$ | $-2e^{2} - 5e$ |
| 53 | $[53, 53, w^{2} + w - 7]$ | $\phantom{-}3e^{2} + 6e - 9$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $\phantom{-}e^{2} + 2e - 14$ |
| 61 | $[61, 61, -3w^{2} + 14]$ | $\phantom{-}e^{2} - 2e - 7$ |
| 61 | $[61, 61, 4w^{2} - 2w - 19]$ | $-5e^{2} - 6e + 7$ |
| 61 | $[61, 61, -2w^{2} + 7]$ | $-3e^{2} + 2e + 11$ |
| 67 | $[67, 67, -2w^{2} - w + 8]$ | $-6e + 1$ |
| 71 | $[71, 71, w^{2} + 2w - 4]$ | $\phantom{-}2e^{2} + 6e - 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w^{2} - 2w - 2]$ | $1$ |