Base field 4.4.6809.1
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[22, 22, -w^{2} + 3]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 15x - 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w^{3} - 4w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{3} - w^{2} - 4w + 3]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e + 4$ |
| 11 | $[11, 11, w^{3} - 5w + 1]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{3} - w^{2} + 5w + 4]$ | $-\frac{1}{2}e^{2} + \frac{3}{2}e + 7$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 5$ |
| 29 | $[29, 29, -w^{2} - w + 3]$ | $-2e + 2$ |
| 31 | $[31, 31, -w^{3} + 6w + 2]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 9$ |
| 43 | $[43, 43, w^{3} - 6w]$ | $\phantom{-}e - 2$ |
| 47 | $[47, 47, 2w^{3} - 9w]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + 9$ |
| 47 | $[47, 47, -2w^{3} + w^{2} + 8w - 2]$ | $\phantom{-}e + 2$ |
| 53 | $[53, 53, -4w^{3} + 2w^{2} + 18w - 5]$ | $-e^{2} + e + 4$ |
| 59 | $[59, 59, w^{2} - w - 5]$ | $\phantom{-}e^{2} - e - 10$ |
| 59 | $[59, 59, 3w^{3} - 15w - 5]$ | $\phantom{-}e^{2} - e - 10$ |
| 71 | $[71, 71, w^{3} - 3w - 3]$ | $-2e + 4$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e - 4$ |
| 83 | $[83, 83, -2w^{3} + 8w + 3]$ | $-e^{2} - e + 6$ |
| 89 | $[89, 89, -2w^{3} + 11w - 2]$ | $-e^{2} - e + 12$ |
| 101 | $[101, 101, 2w^{3} - w^{2} - 10w]$ | $-2e - 6$ |
| 101 | $[101, 101, 2w^{3} - 2w^{2} - 10w + 3]$ | $\phantom{-}2e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 1]$ | $-1$ |
| $11$ | $[11, 11, w^{3} - 5w + 1]$ | $-1$ |