Base field 3.3.1396.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[5, 5, w]$ |
| Dimension: | $3$ |
| 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:
| \(x^{3} - x^{2} - 5x + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-1$ |
| 5 | $[5, 5, -w^{2} + 6]$ | $\phantom{-}e^{2} - e - 4$ |
| 5 | $[5, 5, -w + 2]$ | $-2$ |
| 7 | $[7, 7, w + 2]$ | $-e^{2} + e + 4$ |
| 11 | $[11, 11, 2w - 1]$ | $-2e$ |
| 13 | $[13, 13, w^{2} + w - 3]$ | $-e - 3$ |
| 27 | $[27, 3, 3]$ | $-e^{2} + 2e + 1$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $-4e + 2$ |
| 41 | $[41, 41, 3w^{2} - w - 23]$ | $-3e^{2} + 11$ |
| 41 | $[41, 41, w^{2} - 2]$ | $-2e^{2} - e + 9$ |
| 43 | $[43, 43, w^{2} - w - 3]$ | $\phantom{-}2e^{2} - 10$ |
| 47 | $[47, 47, -w - 4]$ | $-e^{2} - 3$ |
| 49 | $[49, 7, 3w^{2} - 2w - 24]$ | $\phantom{-}3e - 5$ |
| 53 | $[53, 53, 2w^{2} - w - 12]$ | $-2e^{2} + 4e + 12$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $\phantom{-}4e^{2} - e - 11$ |
| 61 | $[61, 61, -w^{2} + 3w - 3]$ | $\phantom{-}3e^{2} - 7$ |
| 71 | $[71, 71, w^{2} + w - 7]$ | $-2e^{2} + 6e + 8$ |
| 79 | $[79, 79, 2w + 3]$ | $\phantom{-}2e^{2} + 4e - 8$ |
| 89 | $[89, 89, 2w - 7]$ | $\phantom{-}5e^{2} - 4e - 17$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w]$ | $1$ |