Base field 4.4.7600.1
Generator \(w\), with minimal polynomial \(x^4 - 9 x^2 + 19\); 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: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^4 - 31 x^2 + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^3 + w^2 + 5 w - 6]$ | $\phantom{-}0$ |
| 9 | $[9, 3, -w^2 - w + 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^2 - w - 4]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w + 1]$ | $-\frac{1}{3} e^3 + \frac{32}{3} e$ |
| 11 | $[11, 11, w - 1]$ | $-\frac{1}{3} e^3 + \frac{32}{3} e$ |
| 19 | $[19, 19, -w]$ | $-\frac{2}{3} e^3 + \frac{64}{3} e$ |
| 19 | $[19, 19, -w^2 - w + 6]$ | $-\frac{1}{3} e^2 + \frac{8}{3}$ |
| 19 | $[19, 19, -w^2 + w + 6]$ | $-\frac{1}{3} e^2 + \frac{8}{3}$ |
| 25 | $[25, 5, 2 w^2 - 9]$ | $\phantom{-}\frac{1}{3} e^2 - \frac{14}{3}$ |
| 29 | $[29, 29, -w^3 + 4 w + 2]$ | $-2$ |
| 29 | $[29, 29, -w^3 + 4 w - 2]$ | $-2$ |
| 41 | $[41, 41, 2 w^2 - w - 7]$ | $\phantom{-}e^3 - 31 e$ |
| 41 | $[41, 41, w^3 - w^2 - 6 w + 4]$ | $\phantom{-}e^3 - 31 e$ |
| 61 | $[61, 61, -w^3 + 3 w^2 + 6 w - 14]$ | $\phantom{-}e^3 - 31 e$ |
| 61 | $[61, 61, w^3 + 2 w^2 - 5 w - 8]$ | $-e^3 + 29 e$ |
| 61 | $[61, 61, -w^3 + 2 w^2 + 5 w - 8]$ | $-e^3 + 29 e$ |
| 61 | $[61, 61, w^3 + 3 w^2 - 6 w - 14]$ | $\phantom{-}e^3 - 31 e$ |
| 89 | $[89, 89, -w^3 + w^2 + 6 w - 9]$ | $-\frac{1}{3} e^2 + \frac{50}{3}$ |
| 89 | $[89, 89, 2 w^3 - w^2 - 10 w + 10]$ | $-\frac{1}{3} e^2 + \frac{50}{3}$ |
| 109 | $[109, 109, -w^3 + 5 w^2 + 7 w - 23]$ | $-\frac{1}{3} e^3 + \frac{35}{3} e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^3 + w^2 + 5 w - 6]$ | $1$ |