Base field 5.5.122821.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[32, 2, 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 6x^{3} - 32x^{2} + 234x - 236\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{4} - 2w^{3} - 3w^{2} + 2w + 1]$ | $\phantom{-}1$ |
| 8 | $[8, 2, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ | $-1$ |
| 11 | $[11, 11, -w^{2} + w + 2]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}2e^{3} - e^{2} - 70e + 86$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + w - 3]$ | $-\frac{2}{3}e^{3} + \frac{2}{3}e^{2} + \frac{71}{3}e - \frac{104}{3}$ |
| 19 | $[19, 19, w^{4} - 2w^{3} - 3w^{2} + w + 2]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{2}{3}e^{2} - \frac{71}{3}e + \frac{110}{3}$ |
| 23 | $[23, 23, w^{4} - 3w^{3} - w^{2} + 5w - 3]$ | $-2$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 2w - 2]$ | $-\frac{5}{3}e^{3} + \frac{2}{3}e^{2} + \frac{176}{3}e - \frac{206}{3}$ |
| 29 | $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 4w - 1]$ | $\phantom{-}2$ |
| 37 | $[37, 37, w^{4} - 3w^{3} - w^{2} + 5w]$ | $-\frac{7}{3}e^{3} + \frac{4}{3}e^{2} + \frac{244}{3}e - \frac{310}{3}$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 4w^{2} + 3w + 1]$ | $-3e^{3} + 2e^{2} + 104e - 136$ |
| 49 | $[49, 7, -2w^{3} + 4w^{2} + 6w - 5]$ | $-\frac{1}{3}e^{3} + \frac{1}{3}e^{2} + \frac{34}{3}e - \frac{52}{3}$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + w^{2} - 7w + 3]$ | $\phantom{-}\frac{7}{3}e^{3} - \frac{4}{3}e^{2} - \frac{241}{3}e + \frac{304}{3}$ |
| 67 | $[67, 67, w^{3} - 2w^{2} - w + 3]$ | $-\frac{2}{3}e^{3} + \frac{2}{3}e^{2} + \frac{71}{3}e - \frac{110}{3}$ |
| 67 | $[67, 67, -w^{4} + 3w^{3} + 2w^{2} - 6w - 1]$ | $-\frac{1}{3}e^{3} + \frac{1}{3}e^{2} + \frac{40}{3}e - \frac{58}{3}$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 4]$ | $-\frac{2}{3}e^{3} + \frac{2}{3}e^{2} + \frac{74}{3}e - \frac{110}{3}$ |
| 83 | $[83, 83, -w^{4} + 3w^{3} + 2w^{2} - 8w - 2]$ | $-e + 10$ |
| 83 | $[83, 83, -w^{4} + 3w^{3} + 2w^{2} - 6w - 2]$ | $-\frac{1}{3}e^{3} - \frac{2}{3}e^{2} + \frac{34}{3}e + \frac{14}{3}$ |
| 103 | $[103, 103, w^{3} - 3w^{2} - 2w + 2]$ | $\phantom{-}\frac{14}{3}e^{3} - \frac{8}{3}e^{2} - \frac{494}{3}e + \frac{644}{3}$ |
| 113 | $[113, 113, -2w^{4} + 4w^{3} + 7w^{2} - 7w - 2]$ | $-3e^{3} + 2e^{2} + 105e - 136$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^{4} - 2w^{3} - 3w^{2} + 2w + 1]$ | $-1$ |
| $8$ | $[8, 2, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ | $1$ |