Base field 4.4.19025.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 13 x^2 + 14 x + 44\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[20, 10, w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $35$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^4 + 4 x^3 + 2 x^2 - 4 x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^2 - 2 w - 6]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^2 + 7]$ | $-1$ |
| 5 | $[5, 5, -\frac{1}{2} w^3 + 2 w^2 + \frac{7}{2} w - 14]$ | $\phantom{-}1$ |
| 5 | $[5, 5, \frac{1}{2} w^3 + \frac{1}{2} w^2 - 6 w - 9]$ | $-e^3 - 3 e^2 + 2$ |
| 11 | $[11, 11, \frac{1}{2} w^3 - 2 w^2 - \frac{5}{2} w + 11]$ | $\phantom{-}2 e^3 + 6 e^2 - 2 e - 6$ |
| 11 | $[11, 11, \frac{1}{2} w^3 + \frac{1}{2} w^2 - 5 w - 7]$ | $-2 e^2 - 3 e + 5$ |
| 31 | $[31, 31, \frac{1}{2} w^2 + \frac{1}{2} w - 4]$ | $-e^3 - 4 e^2 - 3 e + 2$ |
| 31 | $[31, 31, -\frac{1}{2} w^2 + \frac{3}{2} w + 3]$ | $\phantom{-}e^3 + 4 e^2 + 5 e - 2$ |
| 41 | $[41, 41, \frac{1}{2} w^2 + \frac{1}{2} w - 6]$ | $\phantom{-}e^3 + 4 e^2 + 3 e - 10$ |
| 41 | $[41, 41, 2 w^3 - \frac{15}{2} w^2 - \frac{25}{2} w + 50]$ | $-4 e^3 - 11 e^2 + e + 8$ |
| 41 | $[41, 41, \frac{5}{2} w^2 - \frac{1}{2} w - 17]$ | $-4 e^2 - 6 e + 6$ |
| 41 | $[41, 41, \frac{1}{2} w^2 - \frac{3}{2} w - 5]$ | $-2 e^3 - 6 e^2 - 4 e + 2$ |
| 61 | $[61, 61, -\frac{1}{2} w^3 + w^2 + \frac{7}{2} w - 1]$ | $-e^3 + 5 e$ |
| 61 | $[61, 61, -\frac{1}{2} w^3 + \frac{1}{2} w^2 + 4 w - 3]$ | $\phantom{-}3 e^3 + 13 e^2 + 9 e - 11$ |
| 71 | $[71, 71, \frac{1}{2} w^3 + w^2 - \frac{11}{2} w - 13]$ | $-4 e^3 - 11 e^2 + 5 e + 6$ |
| 71 | $[71, 71, -\frac{1}{2} w^3 + \frac{5}{2} w^2 + 2 w - 17]$ | $\phantom{-}3 e^3 + 13 e^2 + 7 e - 13$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}6$ |
| 89 | $[89, 89, -w^3 + \frac{3}{2} w^2 + \frac{13}{2} w - 9]$ | $\phantom{-}6 e^3 + 17 e^2 + 4 e - 1$ |
| 89 | $[89, 89, w^3 - \frac{7}{2} w^2 - \frac{11}{2} w + 20]$ | $\phantom{-}e^3 + 6 e^2 + 6 e - 3$ |
| 89 | $[89, 89, -w^3 - \frac{1}{2} w^2 + \frac{19}{2} w + 12]$ | $\phantom{-}3 e^3 + 12 e^2 + 5 e - 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^2 + 7]$ | $1$ |
| $5$ | $[5, 5, -\frac{1}{2} w^3 + 2 w^2 + \frac{7}{2} w - 14]$ | $-1$ |