Base field 4.4.17417.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 3x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[20, 20, w^{3} - 2w^{2} - 3w]$ |
| Dimension: | $5$ |
| 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:
| \(x^{5} - 2x^{4} - 8x^{3} + 8x^{2} + 20x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - 3w^{2} - w + 2]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w^{2} - 2w - 3]$ | $-1$ |
| 5 | $[5, 5, w^{3} - 3w^{2} - 3w + 5]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}e^{3} - e^{2} - 5e - 1$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $-e^{4} + 3e^{3} + 3e^{2} - 9e - 2$ |
| 17 | $[17, 17, -w^{2} + 3w + 1]$ | $-e^{3} + 6e + 4$ |
| 23 | $[23, 23, w^{2} - 3]$ | $\phantom{-}e^{4} - 3e^{3} - 3e^{2} + 10e$ |
| 25 | $[25, 5, -w^{2} + 2w + 1]$ | $\phantom{-}e^{4} - 3e^{3} - 5e^{2} + 12e + 6$ |
| 37 | $[37, 37, w^{3} - 4w^{2} - 2w + 9]$ | $-e^{4} + 2e^{3} + 4e^{2} - 6e - 2$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-e^{4} + 3e^{3} + 5e^{2} - 14e - 6$ |
| 49 | $[49, 7, -w^{3} + 2w^{2} + 2w - 1]$ | $-2e^{3} + 3e^{2} + 7e - 4$ |
| 49 | $[49, 7, w^{2} + w - 3]$ | $-e^{4} + 3e^{3} + 3e^{2} - 8e - 6$ |
| 59 | $[59, 59, w^{3} - 3w^{2} - 4w + 5]$ | $\phantom{-}2e^{4} - 6e^{3} - 10e^{2} + 22e + 16$ |
| 67 | $[67, 67, -w^{3} + 3w^{2} + w - 5]$ | $-2e^{4} + 7e^{3} + 6e^{2} - 23e - 6$ |
| 71 | $[71, 71, 2w - 3]$ | $\phantom{-}e^{4} - 3e^{3} - 4e^{2} + 10e + 4$ |
| 71 | $[71, 71, w^{3} - 4w^{2} + 2w + 5]$ | $\phantom{-}2e^{4} - 8e^{3} - 4e^{2} + 30e + 6$ |
| 79 | $[79, 79, -w^{3} + 5w^{2} - 4w - 5]$ | $\phantom{-}3e^{2} - 7e - 14$ |
| 79 | $[79, 79, -2w^{3} + 7w^{2} + 5w - 15]$ | $\phantom{-}3e^{3} - 3e^{2} - 14e$ |
| 81 | $[81, 3, -3]$ | $-2e^{4} + 3e^{3} + 14e^{2} - 13e - 14$ |
| 83 | $[83, 83, -2w^{3} + 6w^{2} + 2w - 5]$ | $\phantom{-}2e^{4} - 4e^{3} - 13e^{2} + 15e + 16$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^{3} - 3w^{2} - w + 2]$ | $-1$ |
| $5$ | $[5, 5, w^{2} - 2w - 3]$ | $1$ |