Base field 4.4.4400.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 16x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{2} + w + 3]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + w^{2} + 4w - 4]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w]$ | $-\frac{1}{2}e^{3} + 6e$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ | $-e^{2} + 10$ |
| 29 | $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ | $-e^{2} + 10$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}0$ |
| 31 | $[31, 31, -w^{3} - w^{2} + 4w + 2]$ | $\phantom{-}0$ |
| 41 | $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ | $\phantom{-}\frac{1}{2}e^{3} - 9e$ |
| 41 | $[41, 41, w^{3} - 5w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - 9e$ |
| 49 | $[49, 7, -w^{3} + w^{2} + 4w - 1]$ | $-\frac{1}{2}e^{3} + 7e$ |
| 49 | $[49, 7, w^{3} + w^{2} - 4w - 1]$ | $-\frac{1}{2}e^{3} + 7e$ |
| 59 | $[59, 59, -3w^{2} - w + 10]$ | $\phantom{-}4$ |
| 59 | $[59, 59, -3w^{2} + w + 10]$ | $\phantom{-}4$ |
| 61 | $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ | $\phantom{-}e^{3} - 15e$ |
| 61 | $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ | $\phantom{-}e^{3} - 15e$ |
| 71 | $[71, 71, 2w^{2} + w - 9]$ | $-8$ |
| 71 | $[71, 71, 2w^{2} - w - 9]$ | $-8$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}2$ |
| 101 | $[101, 101, 2w^{2} - w - 10]$ | $-e^{2} + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{2} + w + 3]$ | $1$ |