Base field 4.4.13625.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 11 x^2 + 12 x + 31\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[20,10,\frac{1}{2} w^2 + \frac{1}{2} w - \frac{7}{2}]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 + 9 x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{1}{2} w^2 - \frac{1}{2} w + \frac{3}{2}]$ | $\phantom{-}1$ |
| 4 | $[4, 2, -\frac{1}{2} w^2 + \frac{3}{2} w + \frac{1}{2}]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w - 3]$ | $-1$ |
| 11 | $[11, 11, \frac{1}{2} w^3 - 4 w - \frac{7}{2}]$ | $\phantom{-}e + 4$ |
| 11 | $[11, 11, -\frac{1}{2} w^3 + \frac{3}{2} w^2 + \frac{5}{2} w - 7]$ | $\phantom{-}e$ |
| 19 | $[19, 19, -w^2 + 2 w + 4]$ | $\phantom{-}e + 4$ |
| 19 | $[19, 19, -w^2 + 5]$ | $\phantom{-}0$ |
| 31 | $[31, 31, w]$ | $\phantom{-}2 e + 8$ |
| 31 | $[31, 31, w + 3]$ | $-e$ |
| 31 | $[31, 31, -w + 4]$ | $-4$ |
| 31 | $[31, 31, w - 1]$ | $-4 e - 20$ |
| 41 | $[41, 41, -w^2 + 2]$ | $\phantom{-}2$ |
| 41 | $[41, 41, \frac{1}{2} w^3 - \frac{5}{2} w^2 - \frac{3}{2} w + 12]$ | $-4 e - 18$ |
| 59 | $[59, 59, \frac{1}{2} w^3 + \frac{1}{2} w^2 - \frac{9}{2} w - 5]$ | $\phantom{-}e - 4$ |
| 59 | $[59, 59, -\frac{1}{2} w^3 + 2 w^2 + 2 w - \frac{17}{2}]$ | $-4 e - 16$ |
| 79 | $[79, 79, -w^2 + 8]$ | $-6 e - 24$ |
| 79 | $[79, 79, w^2 - 2 w - 7]$ | $-2 e - 4$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}2 e + 2$ |
| 101 | $[101, 101, -w^3 + \frac{1}{2} w^2 + \frac{15}{2} w + \frac{3}{2}]$ | $-2 e - 6$ |
| 101 | $[101, 101, w^3 - \frac{5}{2} w^2 - \frac{11}{2} w + \frac{17}{2}]$ | $-5 e - 18$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4,2,-\frac{1}{2} w^2 - \frac{1}{2} w + \frac{3}{2}]$ | $-1$ |
| $5$ | $[5,5,-w - 2]$ | $1$ |