Base field 4.4.4913.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[47, 47, -w^{2} + 2]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + x^{2} - 6x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{1}{2}w^{3} + 3w + \frac{5}{2}]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w^{3} - w^{2} - 6w]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -\frac{1}{2}w^{3} + w^{2} + 3w - \frac{1}{2}]$ | $-\frac{3}{2}e^{2} + \frac{1}{2}e + 7$ |
| 13 | $[13, 13, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{7}{2}]$ | $-\frac{1}{2}e^{2} + \frac{3}{2}e + 5$ |
| 13 | $[13, 13, -\frac{1}{2}w^{3} + 4w - \frac{1}{2}]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 2$ |
| 13 | $[13, 13, -\frac{1}{2}w^{3} + 4w + \frac{5}{2}]$ | $-e^{2} - e + 4$ |
| 17 | $[17, 17, \frac{1}{2}w^{3} - w^{2} - w + \frac{3}{2}]$ | $\phantom{-}2$ |
| 47 | $[47, 47, -w^{2} + 2]$ | $-1$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 5]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e + 4$ |
| 47 | $[47, 47, -\frac{3}{2}w^{3} + w^{2} + 10w + \frac{3}{2}]$ | $-2e^{2} - 2e + 12$ |
| 47 | $[47, 47, -\frac{1}{2}w^{3} + 5w - \frac{1}{2}]$ | $\phantom{-}e^{2} - e$ |
| 67 | $[67, 67, \frac{3}{2}w^{3} - 2w^{2} - 8w + \frac{3}{2}]$ | $\phantom{-}\frac{3}{2}e^{2} - \frac{1}{2}e - 1$ |
| 67 | $[67, 67, \frac{1}{2}w^{3} - 2w - \frac{5}{2}]$ | $-\frac{5}{2}e^{2} + \frac{1}{2}e + 10$ |
| 67 | $[67, 67, -\frac{1}{2}w^{3} + w^{2} + w - \frac{5}{2}]$ | $-\frac{5}{2}e^{2} + \frac{1}{2}e + 10$ |
| 67 | $[67, 67, -\frac{3}{2}w^{3} + w^{2} + 9w - \frac{1}{2}]$ | $\phantom{-}4e$ |
| 81 | $[81, 3, -3]$ | $-\frac{3}{2}e^{2} - \frac{1}{2}e + 8$ |
| 89 | $[89, 89, w^{2} - 2w - 4]$ | $-2e^{2} + 8$ |
| 89 | $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - 9w + \frac{3}{2}]$ | $\phantom{-}\frac{3}{2}e^{2} + \frac{5}{2}e - 10$ |
| 89 | $[89, 89, -\frac{1}{2}w^{3} + w^{2} + 4w - \frac{7}{2}]$ | $-\frac{1}{2}e^{2} + \frac{7}{2}e + 7$ |
| 89 | $[89, 89, -w^{3} + 7w + 1]$ | $-2e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $47$ | $[47, 47, -w^{2} + 2]$ | $1$ |