Base field 4.4.19796.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 8\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ |
| 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:
| \(x^{5} + 2x^{4} - 3x^{3} - 5x^{2} + x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 2]$ | $\phantom{-}e^{4} + 2e^{3} - 3e^{2} - 4e + 1$ |
| 2 | $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ | $-1$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ | $\phantom{-}3$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $-e^{4} + 6e^{2} - e - 5$ |
| 19 | $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}4e^{4} + 6e^{3} - 12e^{2} - 11e + 5$ |
| 23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}e^{4} + 2e^{3} - 2e^{2} - 6e - 1$ |
| 31 | $[31, 31, -w^{2} + w + 1]$ | $\phantom{-}4e^{4} + 3e^{3} - 18e^{2} - 5e + 11$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}2e^{4} + 3e^{3} - 9e^{2} - 7e + 7$ |
| 49 | $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ | $-4e^{4} - 6e^{3} + 9e^{2} + 11e + 4$ |
| 53 | $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ | $\phantom{-}e^{4} - 2e^{3} - 5e^{2} + 8e + 2$ |
| 53 | $[53, 53, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}5e^{4} + 9e^{3} - 13e^{2} - 17e$ |
| 61 | $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ | $-3e^{3} - 3e^{2} + 9e$ |
| 61 | $[61, 61, 2w^{2} - 7]$ | $-3e^{4} - 3e^{3} + 15e^{2} + 6e - 6$ |
| 71 | $[71, 71, w^{2} - 3w - 5]$ | $-e^{4} - e^{3} + e^{2} + 2e + 5$ |
| 73 | $[73, 73, 2w - 3]$ | $\phantom{-}e^{4} - 6e^{2} + e + 11$ |
| 73 | $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ | $-3e + 3$ |
| 79 | $[79, 79, 2w^{2} - 5]$ | $-6e^{4} - 11e^{3} + 16e^{2} + 20e - 2$ |
| 81 | $[81, 3, -3]$ | $-2e^{4} + 12e^{2} + e - 10$ |
| 101 | $[101, 101, 2w^{2} - 4w - 9]$ | $\phantom{-}6e^{4} + 15e^{3} - 12e^{2} - 33e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ | $1$ |