Base field 4.4.13625.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 11x^{2} + 12x + 31\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16,4,-\frac{1}{2}w^{2} + \frac{3}{2}w + \frac{3}{2}]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 18x^{2} + 76\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + \frac{3}{2}]$ | $\phantom{-}0$ |
| 4 | $[4, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w + \frac{1}{2}]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 3]$ | $-e$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{7}{2}]$ | $-\frac{1}{2}e^{2} + 3$ |
| 11 | $[11, 11, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$ | $-\frac{1}{2}e^{2} + 1$ |
| 19 | $[19, 19, -w^{2} + 2w + 4]$ | $-\frac{1}{2}e^{3} + 4e$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $\phantom{-}\frac{1}{2}e^{3} - 4e$ |
| 31 | $[31, 31, w]$ | $-\frac{1}{2}e^{2} + 2$ |
| 31 | $[31, 31, w + 3]$ | $\phantom{-}\frac{3}{2}e^{2} - 16$ |
| 31 | $[31, 31, -w + 4]$ | $-\frac{3}{2}e^{2} + 18$ |
| 31 | $[31, 31, w - 1]$ | $\phantom{-}\frac{3}{2}e^{2} - 18$ |
| 41 | $[41, 41, -w^{2} + 2]$ | $\phantom{-}\frac{9}{2}e^{2} - 39$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{3}{2}w + 12]$ | $-\frac{7}{2}e^{2} + 31$ |
| 59 | $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 5]$ | $-\frac{1}{2}e^{3} + 5e$ |
| 59 | $[59, 59, -\frac{1}{2}w^{3} + 2w^{2} + 2w - \frac{17}{2}]$ | $-\frac{3}{2}e^{3} + 15e$ |
| 79 | $[79, 79, -w^{2} + 8]$ | $\phantom{-}\frac{1}{2}e^{3} - 7e$ |
| 79 | $[79, 79, w^{2} - 2w - 7]$ | $\phantom{-}\frac{3}{2}e^{3} - 15e$ |
| 81 | $[81, 3, -3]$ | $-\frac{1}{2}e^{2} + 3$ |
| 101 | $[101, 101, -w^{3} + \frac{1}{2}w^{2} + \frac{15}{2}w + \frac{3}{2}]$ | $\phantom{-}\frac{3}{2}e^{2} - 18$ |
| 101 | $[101, 101, w^{3} - \frac{5}{2}w^{2} - \frac{11}{2}w + \frac{17}{2}]$ | $\phantom{-}\frac{3}{2}e^{2} - 30$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4,2,-\frac{1}{2}w^{2} - \frac{1}{2}w + \frac{3}{2}]$ | $-1$ |