Base field 4.4.9301.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[7, 7, -w^{2} + 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 10x^{3} + 17x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + w^{2} + 4w + 1]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} - 4$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $-1$ |
| 7 | $[7, 7, -w^{2} + w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e$ |
| 16 | $[16, 2, 2]$ | $-e^{4} + 8e^{2} - e - 5$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}2e - 2$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}e^{3} - e^{2} - 7e + 4$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 5w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{9}{2}e^{2} + \frac{9}{2}e + 4$ |
| 37 | $[37, 37, -w^{3} + 4w + 1]$ | $-e^{4} + e^{3} + 9e^{2} - 9e - 14$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - \frac{13}{2}e^{2} + 9e + 12$ |
| 49 | $[49, 7, -w^{3} + 3w^{2} + 2w - 4]$ | $\phantom{-}e^{3} + 2e^{2} - 7e - 6$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 4w - 2]$ | $-3e - 2$ |
| 61 | $[61, 61, -w^{3} + 3w^{2} + 2w - 7]$ | $-e^{4} + 9e^{2} + 2e - 14$ |
| 67 | $[67, 67, w^{2} - 3w - 2]$ | $-2e + 4$ |
| 71 | $[71, 71, -w^{2} + 5]$ | $-e^{4} + e^{3} + 7e^{2} - 9e - 4$ |
| 71 | $[71, 71, 2w^{3} - w^{2} - 9w - 2]$ | $-\frac{3}{2}e^{4} - \frac{1}{2}e^{3} + \frac{27}{2}e^{2} + \frac{1}{2}e - 12$ |
| 71 | $[71, 71, w^{2} - 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{13}{2}e^{2} + \frac{5}{2}e + 16$ |
| 79 | $[79, 79, w^{2} - 3w - 1]$ | $-e^{3} - 2e^{2} + 7e$ |
| 79 | $[79, 79, w^{3} - 6w - 1]$ | $-e^{4} + \frac{3}{2}e^{3} + 11e^{2} - \frac{19}{2}e - 16$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 3w - 7]$ | $\phantom{-}e^{4} + \frac{3}{2}e^{3} - 9e^{2} - \frac{19}{2}e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w^{2} + 2]$ | $1$ |