Base field 4.4.11344.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 4x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[20, 10, -w^{3} + 2w^{2} + w - 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - x^{3} - 7x^{2} + 5x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w + 2]$ | $-e^{3} - e^{2} + 5e + 4$ |
| 27 | $[27, 3, -w^{3} + 2w^{2} + 4w - 4]$ | $-e^{3} + 2e^{2} + 4e - 4$ |
| 29 | $[29, 29, -w^{2} + 3w + 1]$ | $\phantom{-}e^{3} - 7e + 2$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 2w + 2]$ | $-2e^{2} + 12$ |
| 31 | $[31, 31, -w^{2} + 2w + 4]$ | $-e^{3} + 5e + 4$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}3e^{3} - 15e$ |
| 49 | $[49, 7, 2w^{3} - 2w^{2} - 8w - 1]$ | $\phantom{-}e^{3} - 5e - 2$ |
| 49 | $[49, 7, w^{3} - w^{2} - 3w - 2]$ | $-2e^{2} + 3e + 10$ |
| 53 | $[53, 53, w^{3} - 3w^{2} - w + 2]$ | $\phantom{-}2e^{3} - 2e^{2} - 10e + 6$ |
| 53 | $[53, 53, w^{3} - 5w - 5]$ | $-3e^{3} + 13e + 6$ |
| 61 | $[61, 61, 2w - 1]$ | $\phantom{-}e^{3} + 2e^{2} - 9e - 6$ |
| 61 | $[61, 61, -w^{3} + 4w^{2} - 4]$ | $\phantom{-}e^{3} + 2e^{2} - 5e - 10$ |
| 67 | $[67, 67, 3w^{3} - 3w^{2} - 13w - 4]$ | $\phantom{-}3e^{3} - 2e^{2} - 13e + 4$ |
| 73 | $[73, 73, -w^{3} + 4w^{2} - 10]$ | $-2e^{2} + e + 6$ |
| 73 | $[73, 73, w^{2} - w + 1]$ | $-e^{2} + 2$ |
| 83 | $[83, 83, -4w^{3} + 5w^{2} + 17w + 1]$ | $\phantom{-}e^{3} + 5e^{2} - 5e - 20$ |
| 83 | $[83, 83, 3w^{3} - 3w^{2} - 14w - 5]$ | $\phantom{-}e^{3} - e^{2} - 5e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w - 1]$ | $-1$ |
| $5$ | $[5, 5, -w + 2]$ | $-1$ |