Base field 3.3.1369.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x - 11\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23,23,-w^{2} + 3w + 8]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $41$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + 2x^{2} - 6x - 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w]$ | $-e^{2} - 2e + 5$ |
| 11 | $[11, 11, -w^{2} + 3w + 7]$ | $\phantom{-}e + 1$ |
| 11 | $[11, 11, w^{2} - 2w - 8]$ | $-2e^{2} - e + 9$ |
| 23 | $[23, 23, w^{2} - 2w - 7]$ | $\phantom{-}2e^{2} + e - 11$ |
| 23 | $[23, 23, w^{2} - 3w - 8]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w - 1]$ | $-2e - 2$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}2e^{2} - 14$ |
| 29 | $[29, 29, w^{2} - 2w - 5]$ | $-2e^{2} + 12$ |
| 29 | $[29, 29, w^{2} - 3w - 10]$ | $-e^{2} - 3e + 4$ |
| 29 | $[29, 29, w - 3]$ | $\phantom{-}e^{2} - 2e - 5$ |
| 31 | $[31, 31, w^{2} - 2w - 6]$ | $-e^{2} + 2e + 7$ |
| 31 | $[31, 31, -w^{2} + 3w + 9]$ | $\phantom{-}e^{2} - e - 6$ |
| 31 | $[31, 31, w - 2]$ | $-e^{2} + e + 10$ |
| 37 | $[37, 37, -w^{2} + 4w + 7]$ | $\phantom{-}e^{2} - 7$ |
| 43 | $[43, 43, 2w^{2} - 6w - 13]$ | $-e^{2} - e$ |
| 43 | $[43, 43, 2w^{2} - 4w - 17]$ | $-e^{2} + 3e + 8$ |
| 43 | $[43, 43, w^{2} - 2w - 12]$ | $-e^{2} - e + 12$ |
| 47 | $[47, 47, w^{2} - 4w - 4]$ | $\phantom{-}e^{2} - 1$ |
| 47 | $[47, 47, w^{2} - w - 5]$ | $\phantom{-}e^{2} - 3e - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23,23,-w^{2} + 3w + 8]$ | $-1$ |