Base field 4.4.16448.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[20, 10, -w^{2} + 2w + 4]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} - 24x^{4} + 128x^{2} - 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ | $-\frac{1}{4}e^{3} + 3e$ |
| 13 | $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ | $-\frac{1}{16}e^{5} + \frac{5}{4}e^{3} - 5e$ |
| 17 | $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ | $-\frac{1}{16}e^{5} + \frac{5}{4}e^{3} - 5e$ |
| 23 | $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ | $-\frac{1}{8}e^{4} + \frac{5}{2}e^{2} - 4$ |
| 25 | $[25, 5, -w^{2} + 3w + 1]$ | $\phantom{-}\frac{1}{16}e^{5} - \frac{5}{4}e^{3} + 3e$ |
| 29 | $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ | $\phantom{-}\frac{1}{8}e^{5} - 3e^{3} + 15e$ |
| 31 | $[31, 31, -w^{2} + 2w + 1]$ | $-\frac{1}{4}e^{3} + 3e$ |
| 43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ | $-\frac{1}{8}e^{4} + \frac{7}{2}e^{2} - 12$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ | $-\frac{1}{8}e^{5} + \frac{13}{4}e^{3} - 17e$ |
| 59 | $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ | $-\frac{1}{8}e^{4} + \frac{3}{2}e^{2} + 4$ |
| 73 | $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ | $-\frac{1}{16}e^{5} + \frac{5}{4}e^{3} - 5e$ |
| 79 | $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ | $\phantom{-}\frac{1}{4}e^{4} - 5e^{2} + 16$ |
| 81 | $[81, 3, -3]$ | $-\frac{1}{4}e^{4} + 5e^{2} - 14$ |
| 83 | $[83, 83, -w - 3]$ | $\phantom{-}\frac{3}{8}e^{4} - \frac{13}{2}e^{2} + 20$ |
| 83 | $[83, 83, w^{2} - 3w - 7]$ | $-e^{2} + 8$ |
| 89 | $[89, 89, w^{2} - 2w - 7]$ | $-\frac{1}{4}e^{4} + 3e^{2} + 2$ |
| 101 | $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ | $-\frac{1}{16}e^{5} + \frac{5}{4}e^{3} - 5e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $5$ | $[5, 5, w - 1]$ | $-1$ |