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: | $[10, 10, w^{3} - 3w^{2} - 3w + 4]$ |
| Dimension: | $3$ |
| 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:
| \(x^{3} + 3x^{2} - 6x - 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ | $\phantom{-}\frac{1}{3}e^{2}$ |
| 13 | $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ | $-\frac{1}{3}e^{2} - e + 1$ |
| 17 | $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ | $\phantom{-}\frac{2}{3}e^{2} - 6$ |
| 23 | $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ | $\phantom{-}\frac{1}{3}e^{2} + 2e$ |
| 25 | $[25, 5, -w^{2} + 3w + 1]$ | $-\frac{1}{3}e^{2} + e + 1$ |
| 29 | $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ | $\phantom{-}\frac{2}{3}e^{2} + e$ |
| 31 | $[31, 31, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{3}e^{2} - e - 5$ |
| 43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ | $\phantom{-}\frac{2}{3}e^{2} + 3e + 2$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ | $-2e^{2} - 3e + 10$ |
| 59 | $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ | $\phantom{-}\frac{2}{3}e^{2} + 6e$ |
| 73 | $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ | $-\frac{4}{3}e^{2} - 2e + 10$ |
| 79 | $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ | $-\frac{8}{3}e^{2} - 4e + 14$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{5}{3}e^{2} + 4e - 2$ |
| 83 | $[83, 83, -w - 3]$ | $-2e^{2} - 6e + 6$ |
| 83 | $[83, 83, w^{2} - 3w - 7]$ | $-\frac{1}{3}e^{2} - e + 9$ |
| 89 | $[89, 89, w^{2} - 2w - 7]$ | $-\frac{7}{3}e^{2} - 4e + 12$ |
| 101 | $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ | $-2e^{2} - 4e + 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $5$ | $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ | $-1$ |