Base field 4.4.13968.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $4$ |
| CM: | yes |
| Base change: | yes |
| Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 29x^{2} - 51x - 18\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 1]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ | $\phantom{-}0$ |
| 9 | $[9, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 2]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{29}{3}e - 12$ |
| 13 | $[13, 13, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{29}{3}e - 12$ |
| 23 | $[23, 23, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w]$ | $\phantom{-}0$ |
| 23 | $[23, 23, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 3]$ | $\phantom{-}0$ |
| 37 | $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w - 3]$ | $\phantom{-}e^{3} - 30e - 26$ |
| 37 | $[37, 37, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 6]$ | $\phantom{-}e^{3} - 30e - 26$ |
| 59 | $[59, 59, -\frac{1}{2}w^{3} + \frac{7}{2}w]$ | $\phantom{-}0$ |
| 59 | $[59, 59, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 3]$ | $\phantom{-}0$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 7w - 7]$ | $-\frac{2}{3}e^{3} + \frac{1}{3}e^{2} + \frac{52}{3}e + 10$ |
| 61 | $[61, 61, w^{3} - w^{2} - 6w + 3]$ | $\phantom{-}e^{3} - 27e - 20$ |
| 61 | $[61, 61, w^{3} - 2w^{2} - 5w + 3]$ | $\phantom{-}e^{3} - 27e - 20$ |
| 61 | $[61, 61, w^{3} - w^{2} - 8w + 1]$ | $-\frac{2}{3}e^{3} + \frac{1}{3}e^{2} + \frac{52}{3}e + 10$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 5]$ | $\phantom{-}0$ |
| 71 | $[71, 71, -w^{3} + \frac{3}{2}w^{2} + \frac{15}{2}w - 6]$ | $\phantom{-}0$ |
| 83 | $[83, 83, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 7]$ | $\phantom{-}0$ |
| 83 | $[83, 83, \frac{1}{2}w^{3} - \frac{7}{2}w - 4]$ | $\phantom{-}0$ |
| 97 | $[97, 97, 2w - 1]$ | $-2e^{3} + 54e + 46$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 1]$ | $-1$ |
| $2$ | $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ | $-1$ |