Base field 3.3.229.1
Generator \(w\), with minimal polynomial \(x^{3} - 4x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[16, 4, w^{2} + w - 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 8x^{2} + 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} + w + 3]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w^{2} - 2]$ | $-e^{3} + 5e$ |
| 13 | $[13, 13, -w^{2} + 2w + 2]$ | $-2e$ |
| 23 | $[23, 23, -2w + 1]$ | $\phantom{-}4$ |
| 27 | $[27, 3, 3]$ | $-2e^{2} + 6$ |
| 29 | $[29, 29, -2w + 3]$ | $\phantom{-}2e^{2} - 8$ |
| 31 | $[31, 31, -2w^{2} + 2w + 3]$ | $\phantom{-}e^{3} - 5e$ |
| 37 | $[37, 37, 4w^{2} - 2w - 13]$ | $\phantom{-}2e^{3} - 12e$ |
| 37 | $[37, 37, -2w^{2} + 5]$ | $\phantom{-}e^{3} - 3e$ |
| 37 | $[37, 37, 2w^{2} - w - 10]$ | $-4e^{2} + 14$ |
| 41 | $[41, 41, w^{2} - 2w - 4]$ | $-e^{3} + 3e$ |
| 47 | $[47, 47, w - 4]$ | $\phantom{-}2e^{2} - 10$ |
| 49 | $[49, 7, 2w^{2} - w - 4]$ | $\phantom{-}2e^{3} - 8e$ |
| 53 | $[53, 53, 2w^{2} - 2w - 7]$ | $-2e$ |
| 53 | $[53, 53, 3w^{2} - 2w - 8]$ | $\phantom{-}e^{3} - 11e$ |
| 53 | $[53, 53, 2w + 5]$ | $-2e^{2} + 12$ |
| 59 | $[59, 59, 2w^{2} - 2w - 9]$ | $-e^{3} + 9e$ |
| 67 | $[67, 67, 2w^{2} - 3]$ | $-2e^{3} + 14e$ |
| 73 | $[73, 73, 2w^{2} + w - 8]$ | $\phantom{-}4e^{2} - 22$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{2} + w + 3]$ | $-1$ |