Base field 4.4.13448.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 4, -w^{2} + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 8x^{2} - 8x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w + 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 4]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 3e + 2$ |
| 5 | $[5, 5, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 10w - 4]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 3e + 2$ |
| 25 | $[25, 5, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 4]$ | $-e^{2} - e + 10$ |
| 37 | $[37, 37, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 4w]$ | $-\frac{3}{2}e^{3} - \frac{1}{2}e^{2} + 13e + 4$ |
| 37 | $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w]$ | $-\frac{3}{2}e^{3} - \frac{1}{2}e^{2} + 13e + 4$ |
| 43 | $[43, 43, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 2]$ | $-2e^{2} + 6$ |
| 43 | $[43, 43, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + 10w + 2]$ | $-2e^{2} + 6$ |
| 49 | $[49, 7, -w^{2} - w + 3]$ | $-\frac{3}{2}e^{3} - \frac{1}{2}e^{2} + 11e + 6$ |
| 49 | $[49, 7, -w^{2} + w + 3]$ | $-\frac{3}{2}e^{3} - \frac{1}{2}e^{2} + 11e + 6$ |
| 59 | $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 2]$ | $\phantom{-}e^{3} + e^{2} - 8e$ |
| 59 | $[59, 59, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 2]$ | $\phantom{-}e^{3} + e^{2} - 8e$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w + 2]$ | $\phantom{-}2e^{3} + e^{2} - 13e - 6$ |
| 61 | $[61, 61, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 8w - 4]$ | $\phantom{-}2e^{3} + e^{2} - 13e - 6$ |
| 73 | $[73, 73, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 2w]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 5e - 4$ |
| 73 | $[73, 73, w^{2} - w + 1]$ | $\phantom{-}\frac{5}{2}e^{3} - \frac{1}{2}e^{2} - 15e - 4$ |
| 73 | $[73, 73, w^{2} + w + 1]$ | $\phantom{-}\frac{5}{2}e^{3} - \frac{1}{2}e^{2} - 15e - 4$ |
| 73 | $[73, 73, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 2w]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 5e - 4$ |
| 81 | $[81, 3, -3]$ | $-2e^{3} + e^{2} + 15e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w + 1]$ | $1$ |