Base field 4.4.15529.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[10, 10, w^{3} - w^{2} - 5w]$ |
| 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:
| \(x^{3} - x^{2} - 12x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}1$ |
| 8 | $[8, 2, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{3} + w^{2} + 5w + 1]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e + 4$ |
| 9 | $[9, 3, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 3$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ | $-e + 1$ |
| 23 | $[23, 23, w^{2} - 2w - 1]$ | $-e + 5$ |
| 29 | $[29, 29, w^{2} - 3w - 1]$ | $-\frac{1}{2}e^{2} + \frac{5}{2}e + 6$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}e - 2$ |
| 37 | $[37, 37, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}e + 1$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}\frac{3}{2}e^{2} - \frac{5}{2}e - 13$ |
| 47 | $[47, 47, -w^{2} + 2w + 5]$ | $-\frac{5}{2}e^{2} + \frac{11}{2}e + 19$ |
| 47 | $[47, 47, 2w^{3} - 2w^{2} - 11w - 5]$ | $\phantom{-}\frac{5}{2}e^{2} - \frac{9}{2}e - 16$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 2w + 1]$ | $-e^{2} + 2e + 5$ |
| 59 | $[59, 59, -w - 3]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}e - 8$ |
| 73 | $[73, 73, w^{2} - w + 1]$ | $\phantom{-}2e$ |
| 73 | $[73, 73, 2w^{3} - 2w^{2} - 12w - 5]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e + 12$ |
| 79 | $[79, 79, 4w^{3} - 4w^{2} - 22w - 7]$ | $-e^{2} + 4e + 13$ |
| 97 | $[97, 97, 2w^{3} - 3w^{2} - 9w + 1]$ | $-2e + 4$ |
| 101 | $[101, 101, 2w^{2} - 2w - 9]$ | $-\frac{3}{2}e^{2} + \frac{7}{2}e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $5$ | $[5, 5, w - 1]$ | $-1$ |