Base field 4.4.16357.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[5, 5, -w^{3} + 5w + 2]$ |
| 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:
| \(x^{4} + 4x^{3} - 8x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + 5w + 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}e^{3} + 3e^{2} - 2e - 4$ |
| 11 | $[11, 11, -w^{3} + 5w]$ | $\phantom{-}e - 2$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 6w - 3]$ | $\phantom{-}e^{2} + e - 4$ |
| 16 | $[16, 2, 2]$ | $-e - 3$ |
| 19 | $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ | $-e^{3} - 3e^{2} + e + 4$ |
| 25 | $[25, 5, -w^{2} + w + 3]$ | $-e^{3} - 4e^{2} + 2$ |
| 27 | $[27, 3, w^{3} - w^{2} - 5w + 4]$ | $-e^{3} - 4e^{2} - 2e + 6$ |
| 31 | $[31, 31, -w - 3]$ | $-2e^{3} - 8e^{2} + 10$ |
| 37 | $[37, 37, -w^{3} - w^{2} + 6w + 4]$ | $-4$ |
| 41 | $[41, 41, w^{3} + w^{2} - 6w - 5]$ | $\phantom{-}2e^{3} + 5e^{2} - 5e - 8$ |
| 43 | $[43, 43, w^{3} - 7w - 2]$ | $-e^{3} - e^{2} + 6e + 2$ |
| 47 | $[47, 47, -2w^{3} + 11w + 2]$ | $-2e^{2} - 4e - 2$ |
| 61 | $[61, 61, w^{2} - 3]$ | $\phantom{-}2e^{2} + 7e$ |
| 67 | $[67, 67, w^{2} + w - 4]$ | $-e^{3} - 3e^{2} + 6e + 6$ |
| 79 | $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ | $\phantom{-}4e^{2} + 8e - 10$ |
| 97 | $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ | $\phantom{-}2e^{3} + 8e^{2} - 2e - 16$ |
| 97 | $[97, 97, -w^{3} + 6w - 3]$ | $-e^{3} + e^{2} + 14e - 2$ |
| 97 | $[97, 97, -3w^{3} + 16w]$ | $\phantom{-}2e^{3} + 4e^{2} - 9e - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w^{3} + 5w + 2]$ | $-1$ |