Base field 4.4.18736.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[21, 21, w^{3} - w^{2} - 5w - 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}1$ |
| 4 | $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-\frac{1}{2}e + 2$ |
| 7 | $[7, 7, w - 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w^{2} - 2w - 4]$ | $\phantom{-}2e$ |
| 23 | $[23, 23, -w^{2} + 2w + 1]$ | $-e$ |
| 23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $-e$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 6w + 2]$ | $\phantom{-}e - 4$ |
| 31 | $[31, 31, -w^{3} + 3w^{2} + w - 1]$ | $-2e + 4$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}4$ |
| 37 | $[37, 37, w^{2} - 2w - 6]$ | $-4$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $-\frac{1}{2}e + 2$ |
| 43 | $[43, 43, w^{2} - 3w - 2]$ | $\phantom{-}e$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 2w - 2]$ | $-\frac{5}{2}e - 2$ |
| 73 | $[73, 73, w^{3} - 3w^{2} - 2w + 3]$ | $\phantom{-}\frac{3}{2}e + 6$ |
| 83 | $[83, 83, -w - 3]$ | $-2e - 4$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}\frac{5}{2}e + 10$ |
| 89 | $[89, 89, 2w - 1]$ | $\phantom{-}\frac{3}{2}e - 6$ |
| 101 | $[101, 101, w^{3} - 4w^{2} + w + 7]$ | $-2e$ |
| 101 | $[101, 101, 2w^{2} - 3w - 3]$ | $-\frac{3}{2}e - 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 1]$ | $-1$ |
| $7$ | $[7, 7, w - 2]$ | $-1$ |