Base field 4.4.6809.1
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[31, 31, -w^{3} + 6w + 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 2x^{4} - 5x^{3} - 10x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} - 4w]$ | $-e^{3} + 5e$ |
| 8 | $[8, 2, w^{3} - w^{2} - 4w + 3]$ | $-e^{3} + 4e$ |
| 11 | $[11, 11, w^{3} - 5w + 1]$ | $\phantom{-}e^{4} + 2e^{3} - 5e^{2} - 10e - 3$ |
| 17 | $[17, 17, -w^{3} - w^{2} + 5w + 4]$ | $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 9e + 2$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $-e^{3} + 5e - 2$ |
| 29 | $[29, 29, -w^{2} - w + 3]$ | $-e^{4} + 4e^{2} - e + 1$ |
| 31 | $[31, 31, -w^{3} + 6w + 2]$ | $\phantom{-}1$ |
| 43 | $[43, 43, w^{3} - 6w]$ | $-2e^{4} - 3e^{3} + 8e^{2} + 14e + 5$ |
| 47 | $[47, 47, 2w^{3} - 9w]$ | $-3e^{4} - 2e^{3} + 17e^{2} + 10e - 7$ |
| 47 | $[47, 47, -2w^{3} + w^{2} + 8w - 2]$ | $\phantom{-}2e^{4} + 5e^{3} - 10e^{2} - 25e + 1$ |
| 53 | $[53, 53, -4w^{3} + 2w^{2} + 18w - 5]$ | $\phantom{-}3e^{4} + 2e^{3} - 18e^{2} - 12e + 7$ |
| 59 | $[59, 59, w^{2} - w - 5]$ | $\phantom{-}e^{4} + 3e^{3} - 4e^{2} - 18e - 7$ |
| 59 | $[59, 59, 3w^{3} - 15w - 5]$ | $-5e^{4} - 6e^{3} + 25e^{2} + 27e - 5$ |
| 71 | $[71, 71, w^{3} - 3w - 3]$ | $\phantom{-}3e^{4} + 2e^{3} - 14e^{2} - 10e - 8$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^{4} + 4e^{3} - 4e^{2} - 16e - 4$ |
| 83 | $[83, 83, -2w^{3} + 8w + 3]$ | $\phantom{-}2e^{4} + 3e^{3} - 10e^{2} - 10e + 4$ |
| 89 | $[89, 89, -2w^{3} + 11w - 2]$ | $\phantom{-}2e^{4} + 5e^{3} - 8e^{2} - 22e - 5$ |
| 101 | $[101, 101, 2w^{3} - w^{2} - 10w]$ | $-5e^{4} - 3e^{3} + 22e^{2} + 13e + 6$ |
| 101 | $[101, 101, 2w^{3} - 2w^{2} - 10w + 3]$ | $\phantom{-}2e^{4} + 2e^{3} - 10e^{2} - 7e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, -w^{3} + 6w + 2]$ | $-1$ |