Base field 4.4.8957.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, w^{3} - w^{2} - 4w]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 12x^{3} + 26x + 10\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + w^{2} + 5w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $-1$ |
| 13 | $[13, 13, -2w^{3} + w^{2} + 11w + 3]$ | $\phantom{-}\frac{2}{5}e^{4} - \frac{3}{5}e^{3} - \frac{22}{5}e^{2} + \frac{23}{5}e + 8$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 4w + 3]$ | $\phantom{-}\frac{2}{5}e^{4} - \frac{3}{5}e^{3} - \frac{22}{5}e^{2} + \frac{23}{5}e + 8$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{5}e^{4} + \frac{4}{5}e^{3} + \frac{16}{5}e^{2} - \frac{34}{5}e - 5$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $-\frac{2}{5}e^{4} - \frac{2}{5}e^{3} + \frac{17}{5}e^{2} + \frac{2}{5}e$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{2}{5}e^{4} - \frac{2}{5}e^{3} + \frac{17}{5}e^{2} + \frac{2}{5}e$ |
| 49 | $[49, 7, -w^{3} + 2w^{2} + 5w - 2]$ | $-\frac{2}{5}e^{4} - \frac{2}{5}e^{3} + \frac{22}{5}e^{2} + \frac{2}{5}e - 10$ |
| 49 | $[49, 7, 2w^{3} - 2w^{2} - 9w - 1]$ | $-\frac{2}{5}e^{4} - \frac{2}{5}e^{3} + \frac{22}{5}e^{2} + \frac{2}{5}e - 10$ |
| 53 | $[53, 53, w^{3} - 3w^{2} + 3]$ | $-\frac{3}{5}e^{4} + \frac{2}{5}e^{3} + \frac{28}{5}e^{2} - \frac{12}{5}e - 2$ |
| 53 | $[53, 53, 2w^{3} - w^{2} - 8w - 3]$ | $-\frac{3}{5}e^{4} + \frac{2}{5}e^{3} + \frac{28}{5}e^{2} - \frac{12}{5}e - 2$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 6w - 1]$ | $\phantom{-}\frac{8}{5}e^{4} - \frac{2}{5}e^{3} - \frac{88}{5}e^{2} + \frac{32}{5}e + 20$ |
| 61 | $[61, 61, -w - 3]$ | $-\frac{2}{5}e^{4} - \frac{2}{5}e^{3} + \frac{22}{5}e^{2} + \frac{12}{5}e - 6$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 5w - 4]$ | $-\frac{2}{5}e^{4} - \frac{2}{5}e^{3} + \frac{22}{5}e^{2} + \frac{12}{5}e - 6$ |
| 79 | $[79, 79, w^{3} - 2w^{2} - 4w + 1]$ | $-2e^{2} - 2e + 10$ |
| 79 | $[79, 79, w^{2} - 5]$ | $-2e^{2} - 2e + 10$ |
| 101 | $[101, 101, w^{3} - 6w]$ | $\phantom{-}2e^{3} + e^{2} - 14e - 6$ |
| 101 | $[101, 101, w^{2} - 2w - 4]$ | $\phantom{-}2e^{3} + e^{2} - 14e - 6$ |
| 103 | $[103, 103, 4w^{3} - 3w^{2} - 20w - 3]$ | $\phantom{-}\frac{2}{5}e^{4} - \frac{8}{5}e^{3} - \frac{22}{5}e^{2} + \frac{58}{5}e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, w^{3} - w^{2} - 4w]$ | $1$ |