Base field 4.4.4400.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[55,55,w^{3} - 3w^{2} - 4w + 11]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 12x^{3} + 27x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{2} + w + 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $-\frac{1}{2}e^{3} + \frac{7}{2}e$ |
| 5 | $[5, 5, -w^{3} + w^{2} + 4w - 4]$ | $-1$ |
| 11 | $[11, 11, w]$ | $-1$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 8$ |
| 29 | $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{9}{2}e^{2} - \frac{9}{2}e + 6$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}2$ |
| 31 | $[31, 31, -w^{3} - w^{2} + 4w + 2]$ | $-\frac{1}{2}e^{3} - e^{2} + \frac{9}{2}e + 4$ |
| 41 | $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ | $\phantom{-}2e + 2$ |
| 41 | $[41, 41, w^{3} - 5w + 2]$ | $-e^{4} + 9e^{2} + 2e - 6$ |
| 49 | $[49, 7, -w^{3} + w^{2} + 4w - 1]$ | $-e^{3} + 2e^{2} + 9e - 10$ |
| 49 | $[49, 7, w^{3} + w^{2} - 4w - 1]$ | $-\frac{1}{2}e^{3} + e^{2} + \frac{5}{2}e - 6$ |
| 59 | $[59, 59, -3w^{2} - w + 10]$ | $\phantom{-}e^{4} + e^{3} - 11e^{2} - 11e + 18$ |
| 59 | $[59, 59, -3w^{2} + w + 10]$ | $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + \frac{13}{2}e^{2} + \frac{27}{2}e - 12$ |
| 61 | $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 10$ |
| 61 | $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{9}{2}e^{2} - \frac{13}{2}e + 6$ |
| 71 | $[71, 71, 2w^{2} + w - 9]$ | $\phantom{-}e^{4} + e^{3} - 11e^{2} - 7e + 16$ |
| 71 | $[71, 71, 2w^{2} - w - 9]$ | $-\frac{1}{2}e^{4} - e^{3} + \frac{9}{2}e^{2} + 8e$ |
| 81 | $[81, 3, -3]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} + e - 2$ |
| 101 | $[101, 101, 2w^{2} - w - 10]$ | $-\frac{1}{2}e^{3} + \frac{7}{2}e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,-w + 1]$ | $1$ |
| $11$ | $[11,11,-w]$ | $1$ |