Base field 4.4.15952.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[8, 2, w^{3} - w^{2} - 5w + 3]$ |
| 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:
| \(x^{5} - 4x^{4} - 3x^{3} + 22x^{2} - 19x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -w^{3} + w^{2} + 5w - 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{3} + 5w + 1]$ | $-2e^{4} + 7e^{3} + 10e^{2} - 39e + 16$ |
| 11 | $[11, 11, -w + 2]$ | $-2e^{4} + 6e^{3} + 11e^{2} - 32e + 12$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 4w + 1]$ | $-2e + 2$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $-e^{3} + 2e^{2} + 7e - 6$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $-e^{4} + 4e^{3} + 4e^{2} - 22e + 10$ |
| 23 | $[23, 23, w^{3} - 6w]$ | $-2e^{4} + 6e^{3} + 12e^{2} - 32e + 8$ |
| 27 | $[27, 3, w^{3} + w^{2} - 5w - 4]$ | $-2e^{4} + 6e^{3} + 10e^{2} - 31e + 16$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 5w]$ | $-2e^{4} + 6e^{3} + 12e^{2} - 32e + 14$ |
| 41 | $[41, 41, 2w^{3} - 11w - 4]$ | $-2e^{3} + 4e^{2} + 13e - 14$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ | $\phantom{-}2e^{4} - 6e^{3} - 12e^{2} + 32e - 6$ |
| 59 | $[59, 59, 2w^{3} - 11w - 2]$ | $\phantom{-}3e^{4} - 10e^{3} - 16e^{2} + 56e - 20$ |
| 67 | $[67, 67, w^{3} - 7w - 1]$ | $\phantom{-}e^{4} - 4e^{3} - 4e^{2} + 26e - 20$ |
| 71 | $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ | $-2e^{4} + 8e^{3} + 8e^{2} - 48e + 24$ |
| 89 | $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ | $\phantom{-}2e^{4} - 5e^{3} - 12e^{2} + 25e - 6$ |
| 101 | $[101, 101, -2w^{3} + 13w + 6]$ | $-2e^{4} + 8e^{3} + 8e^{2} - 50e + 30$ |
| 101 | $[101, 101, w^{3} + w^{2} - 6w - 3]$ | $\phantom{-}4e^{4} - 14e^{3} - 20e^{2} + 82e - 34$ |
| 101 | $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ | $-4e^{4} + 14e^{3} + 20e^{2} - 76e + 34$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 1]$ | $1$ |