Base field 3.3.697.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[25, 5, w^{2} - 7]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 2x^{3} - 7x^{2} - x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-e - 1$ |
| 11 | $[11, 11, -w^{2} + 2w + 4]$ | $-e^{2} + 2e + 4$ |
| 11 | $[11, 11, -w + 2]$ | $-e^{3} + 3e^{2} + 4e$ |
| 11 | $[11, 11, w - 1]$ | $-e + 2$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-2e^{3} + 5e^{2} + 10e - 2$ |
| 17 | $[17, 17, -w^{2} + w + 8]$ | $-2e^{3} + 6e^{2} + 8e - 6$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}e^{3} - 2e^{2} - 8e + 2$ |
| 19 | $[19, 19, -w^{2} + 6]$ | $\phantom{-}e^{3} - 4e^{2} - 2e + 8$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}2e^{3} - 5e^{2} - 9e + 2$ |
| 25 | $[25, 5, w^{2} - 7]$ | $\phantom{-}1$ |
| 27 | $[27, 3, -3]$ | $-e^{3} + 2e^{2} + 7e + 2$ |
| 31 | $[31, 31, w^{2} - 2w - 8]$ | $\phantom{-}e^{3} - e^{2} - 9e + 2$ |
| 37 | $[37, 37, w^{2} - 2w - 6]$ | $\phantom{-}2e^{3} - 7e^{2} - 4e + 10$ |
| 41 | $[41, 41, -w - 4]$ | $-2e^{3} + 5e^{2} + 12e - 2$ |
| 41 | $[41, 41, w^{2} - 2w - 7]$ | $-e^{3} + 3e^{2} + 4e - 2$ |
| 47 | $[47, 47, 2w^{2} - 3w - 7]$ | $-e^{2} + 4$ |
| 53 | $[53, 53, -w^{2} + w + 9]$ | $\phantom{-}e^{3} - e^{2} - 9e - 8$ |
| 61 | $[61, 61, 3w^{2} - 2w - 17]$ | $-e^{3} + 3e^{2} + 3e + 8$ |
| 67 | $[67, 67, 2w - 1]$ | $-e^{2} + 6e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, w^{2} - 7]$ | $-1$ |