Base field 5.5.186037.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 2x^{2} + 5x - 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[25, 5, -w^{2} + w + 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $58$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 6x^{2} - 4x + 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 5]$ | $-1$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $-e^{3} + e^{2} + 5e - 4$ |
| 16 | $[16, 2, w^{4} - w^{3} - 6w^{2} + 2w + 5]$ | $-2e^{2} - 2e + 6$ |
| 19 | $[19, 19, -w^{4} + 7w^{2} + 2w - 3]$ | $\phantom{-}e^{2} + 2e - 7$ |
| 23 | $[23, 23, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}2e^{3} - 7e - 1$ |
| 23 | $[23, 23, -w^{4} + 7w^{2} + 4w - 7]$ | $\phantom{-}e + 1$ |
| 25 | $[25, 5, -w^{2} + w + 3]$ | $-1$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $\phantom{-}e^{3} - 2e^{2} - 5e + 10$ |
| 31 | $[31, 31, w^{4} - 6w^{2} - 2w + 3]$ | $-3e^{2} + 9$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 4w + 3]$ | $-2e^{3} + e^{2} + 6e - 4$ |
| 67 | $[67, 67, 2w^{3} - 3w^{2} - 8w + 3]$ | $\phantom{-}e^{3} - e^{2} + 5$ |
| 79 | $[79, 79, -w^{4} + 6w^{2} + 3w - 1]$ | $\phantom{-}e^{3} + 4e^{2} - 6e - 7$ |
| 83 | $[83, 83, 2w^{4} - 14w^{2} - 7w + 11]$ | $\phantom{-}3e^{3} - e^{2} - 10e + 7$ |
| 83 | $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $-e^{3} + 3e - 3$ |
| 83 | $[83, 83, -w^{4} + 8w^{2} + 3w - 7]$ | $\phantom{-}3e^{3} - 14e + 3$ |
| 97 | $[97, 97, w^{4} - 2w^{3} - 4w^{2} + 4w + 1]$ | $-4e^{3} - e^{2} + 15e - 5$ |
| 101 | $[101, 101, 2w^{4} - 14w^{2} - 6w + 11]$ | $-4e^{3} - 3e^{2} + 15e + 10$ |
| 101 | $[101, 101, -w^{4} + 8w^{2} + 2w - 9]$ | $-4e^{3} - 4e^{2} + 12e + 13$ |
| 107 | $[107, 107, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}2e^{3} - 3e^{2} - 11e + 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, -w^{2} + w + 3]$ | $1$ |