Base field 4.4.12197.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[5, 5, -w + 2]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + 4x^{2} - x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 2]$ | $-1$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $-2e - 2$ |
| 13 | $[13, 13, w^{3} - w^{2} - 4w]$ | $\phantom{-}e^{2} + 3e - 3$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}e^{2} + 3e - 1$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $-e^{2} - 4e - 1$ |
| 19 | $[19, 19, w^{3} - 5w]$ | $-e^{2} - 2e$ |
| 19 | $[19, 19, -w + 3]$ | $\phantom{-}3$ |
| 23 | $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ | $\phantom{-}3e + 4$ |
| 23 | $[23, 23, w^{2} - 2]$ | $\phantom{-}e^{2} + 2e + 1$ |
| 25 | $[25, 5, w^{2} - 3]$ | $\phantom{-}4$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ | $-3e^{2} - 6e + 7$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 6w - 4]$ | $\phantom{-}e^{2} + 2e - 1$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}2e^{2} + 2e - 8$ |
| 47 | $[47, 47, w^{3} - 6w + 1]$ | $\phantom{-}e^{2} - 2e - 9$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $-2e^{2} + 16$ |
| 67 | $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ | $-e^{2} + 9$ |
| 67 | $[67, 67, w^{3} - 7w + 3]$ | $-e^{2} + 17$ |
| 73 | $[73, 73, 2w^{3} - w^{2} - 9w]$ | $\phantom{-}2e^{2} + 4e - 2$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^{2} - 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w + 2]$ | $1$ |