Base field 3.3.564.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[26, 26, -w^{2} - w + 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 3x^{3} - 7x^{2} + 22x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 1]$ | $-1$ |
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{7}{2}e + 3$ |
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{2} - 2w - 2]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{2} + 2]$ | $\phantom{-}e^{3} - 9e + 2$ |
| 19 | $[19, 19, -w^{2} + w + 1]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{5}{2}e + 5$ |
| 31 | $[31, 31, -w + 4]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - \frac{9}{2}e - 6$ |
| 41 | $[41, 41, -w^{2} + 2w - 2]$ | $\phantom{-}e^{3} - e^{2} - 10e + 10$ |
| 41 | $[41, 41, -2w^{2} - 3w + 4]$ | $-\frac{3}{2}e^{3} + \frac{1}{2}e^{2} + \frac{19}{2}e - 1$ |
| 41 | $[41, 41, 2w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - \frac{9}{2}e + 10$ |
| 43 | $[43, 43, -w^{2} - w + 5]$ | $-\frac{3}{2}e^{3} + \frac{1}{2}e^{2} + \frac{19}{2}e + 4$ |
| 47 | $[47, 47, -w^{2} + 8]$ | $-e^{3} + e^{2} + 7e - 10$ |
| 47 | $[47, 47, 2w^{2} - w - 8]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{13}{2}e - 2$ |
| 53 | $[53, 53, w^{2} + w - 7]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - \frac{5}{2}e + 12$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $-2e^{3} + 15e + 2$ |
| 61 | $[61, 61, -3w^{2} + 14]$ | $-\frac{1}{2}e^{3} + \frac{5}{2}e^{2} + \frac{5}{2}e - 10$ |
| 61 | $[61, 61, 4w^{2} - 2w - 19]$ | $-e^{3} + e^{2} + 7e - 8$ |
| 61 | $[61, 61, -2w^{2} + 7]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - \frac{3}{2}e + 15$ |
| 67 | $[67, 67, -2w^{2} - w + 8]$ | $-2e^{3} - e^{2} + 14e + 12$ |
| 71 | $[71, 71, w^{2} + 2w - 4]$ | $-\frac{3}{2}e^{3} - \frac{1}{2}e^{2} + \frac{23}{2}e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w - 1]$ | $1$ |
| $13$ | $[13, 13, w^{2} - 2w - 2]$ | $-1$ |