Base field 3.3.733.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 8\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[20, 20, w^{2} - 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} - 12x^{2} - 20x + 17\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 2]$ | $\phantom{-}0$ |
| 4 | $[4, 2, -w^{2} - w + 5]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 3]$ | $-1$ |
| 7 | $[7, 7, -w^{2} - 2w + 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{9}{2}e + \frac{9}{2}$ |
| 11 | $[11, 11, -w^{2} + 5]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{11}{2}e - \frac{3}{2}$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}e^{2} - 5$ |
| 23 | $[23, 23, w^{2} - 3]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{7}{2}e + \frac{7}{2}$ |
| 25 | $[25, 5, w^{2} + 2w - 1]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{9}{2}e + \frac{13}{2}$ |
| 27 | $[27, 3, -3]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{7}{2}e + \frac{3}{2}$ |
| 29 | $[29, 29, -3w + 7]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{11}{2}e + \frac{15}{2}$ |
| 43 | $[43, 43, -3w^{2} - 2w + 17]$ | $\phantom{-}e^{3} - 11e - 2$ |
| 49 | $[49, 7, -2w^{2} + w + 11]$ | $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + \frac{11}{2}e + \frac{17}{2}$ |
| 67 | $[67, 67, -2w^{2} - 4w + 3]$ | $-e^{3} + 9e + 4$ |
| 71 | $[71, 71, -2w^{2} + w + 9]$ | $\phantom{-}e^{2} + 2e - 5$ |
| 73 | $[73, 73, w^{2} + 2w - 7]$ | $\phantom{-}e^{3} - e^{2} - 7e + 9$ |
| 73 | $[73, 73, -2w^{2} - 2w + 11]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - \frac{7}{2}e - \frac{17}{2}$ |
| 73 | $[73, 73, w - 5]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{1}{2}e^{2} - \frac{33}{2}e - \frac{1}{2}$ |
| 89 | $[89, 89, 2w^{2} + w - 9]$ | $-e^{3} - e^{2} + 7e + 7$ |
| 89 | $[89, 89, -w^{2} - 2w + 9]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{13}{2}e + \frac{25}{2}$ |
| 89 | $[89, 89, -2w - 1]$ | $-e^{3} - 2e^{2} + 11e + 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 2]$ | $-1$ |
| $5$ | $[5, 5, -w + 3]$ | $1$ |