Base field 3.3.785.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[25, 5, w^{2} + 2w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 8x^{2} + 4x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -w + 3]$ | $-1$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{3} - 4e + 1$ |
| 9 | $[9, 3, w^{2} + w - 4]$ | $\phantom{-}e^{3} + e^{2} - 6e$ |
| 13 | $[13, 13, w + 3]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 4e + 3$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $-\frac{1}{2}e^{2} + e + 1$ |
| 23 | $[23, 23, w^{2} - 2]$ | $-e^{3} - \frac{3}{2}e^{2} + 7e + 1$ |
| 23 | $[23, 23, w^{2} - 3]$ | $-e^{3} + 8e - 2$ |
| 23 | $[23, 23, -w^{2} + 8]$ | $-\frac{1}{2}e^{2} + e + 3$ |
| 29 | $[29, 29, w - 4]$ | $\phantom{-}e^{3} - 7e + 2$ |
| 37 | $[37, 37, w^{2} + w - 8]$ | $-e^{3} - 2e^{2} + 4e + 8$ |
| 41 | $[41, 41, w^{2} + 2w - 4]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - 2e + 1$ |
| 47 | $[47, 47, 2w^{2} + w - 8]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - 4e - 7$ |
| 59 | $[59, 59, -2w^{2} - 3w + 6]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 2e + 3$ |
| 61 | $[61, 61, -2w - 1]$ | $\phantom{-}3e^{3} + \frac{5}{2}e^{2} - 17e + 1$ |
| 67 | $[67, 67, -2w - 3]$ | $-e^{3} - 2e^{2} + 2e + 8$ |
| 79 | $[79, 79, 2w^{2} - 9]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + 6e - 5$ |
| 109 | $[109, 109, w^{2} + 2w - 6]$ | $-2e^{3} - 3e^{2} + 8e + 8$ |
| 109 | $[109, 109, 2w^{2} + w - 14]$ | $\phantom{-}2e^{2} - 3e - 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w]$ | $-1$ |
| $5$ | $[5, 5, -w + 3]$ | $1$ |