Base field 4.4.8000.1
Generator \(w\), with minimal polynomial \(x^4 - 10 x^2 + 20\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[44, 22, -w^2 + w + 6]$ |
| Dimension: | $4$ |
| 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:
| \(x^4 + 3 x^3 - 4 x^2 - 11 x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2} w^3 - 3 w + 2]$ | $-1$ |
| 5 | $[5, 5, w^2 - w - 5]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -\frac{1}{2} w^3 - \frac{1}{2} w^2 + 3 w + 3]$ | $\phantom{-}2 e^2 + 2 e - 7$ |
| 11 | $[11, 11, -\frac{1}{2} w^2 + w + 2]$ | $\phantom{-}e^3 + e^2 - 5 e - 2$ |
| 11 | $[11, 11, -\frac{1}{2} w^2 - w + 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, \frac{1}{2} w^3 - \frac{1}{2} w^2 - 3 w + 3]$ | $-e^3 - 2 e^2 + 2 e + 3$ |
| 29 | $[29, 29, -\frac{1}{2} w^2 - w + 4]$ | $\phantom{-}e^3 + 3 e^2 - e - 10$ |
| 29 | $[29, 29, -\frac{1}{2} w^3 + \frac{1}{2} w^2 + 3 w - 1]$ | $-e^3 - 3 e^2 + 4 e + 9$ |
| 29 | $[29, 29, -\frac{1}{2} w^3 - \frac{1}{2} w^2 + 3 w + 1]$ | $-2 e - 1$ |
| 29 | $[29, 29, -\frac{1}{2} w^2 + w + 4]$ | $-e^3 + 6 e - 5$ |
| 41 | $[41, 41, w^3 - \frac{1}{2} w^2 - 6 w + 6]$ | $-e^2 + e + 2$ |
| 41 | $[41, 41, -\frac{1}{2} w^3 + \frac{5}{2} w^2 + 5 w - 14]$ | $\phantom{-}e^3 - e^2 - 6 e + 12$ |
| 41 | $[41, 41, \frac{1}{2} w^3 - \frac{1}{2} w^2 - 3 w + 6]$ | $\phantom{-}e^3 + 2 e^2 - 5 e - 8$ |
| 41 | $[41, 41, -\frac{3}{2} w^2 - 2 w + 6]$ | $\phantom{-}2 e^3 + e^2 - 11 e + 3$ |
| 79 | $[79, 79, -w^3 - w^2 + 4 w - 1]$ | $-3 e^2 - 3 e + 10$ |
| 79 | $[79, 79, -\frac{3}{2} w^2 - w + 9]$ | $\phantom{-}2 e^3 + e^2 - 13 e - 8$ |
| 79 | $[79, 79, -w^3 + \frac{7}{2} w^2 + 9 w - 21]$ | $-e^3 - 4 e^2 - e + 6$ |
| 79 | $[79, 79, w^3 - w^2 - 6 w + 9]$ | $-2 e^3 - 2 e^2 + 13 e + 7$ |
| 81 | $[81, 3, -3]$ | $-e^3 - 5 e^2 + 2 e + 17$ |
| 109 | $[109, 109, w^2 - w - 7]$ | $\phantom{-}2 e^3 + 2 e^2 - 9 e - 9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, \frac{1}{2} w^3 - 3 w + 2]$ | $1$ |
| $11$ | $[11, 11, -\frac{1}{2} w^2 - w + 2]$ | $-1$ |