Base field 4.4.725.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 3 x^2 + x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[131, 131, -3 w^3 + 2 w^2 + 8 w - 2]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - 4 x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, -w^3 + 2 w^2 + w - 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^3 - 3 w]$ | $-e + 2$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{2} e + 1$ |
| 19 | $[19, 19, -w^3 + 2 w + 2]$ | $\phantom{-}\frac{1}{2} e + 3$ |
| 19 | $[19, 19, 2 w^3 - 3 w^2 - 4 w + 2]$ | $-e - 1$ |
| 25 | $[25, 5, 2 w^3 - 2 w^2 - 4 w + 1]$ | $\phantom{-}\frac{3}{2} e - 3$ |
| 29 | $[29, 29, w^3 - w^2 - 4 w + 1]$ | $-e - 2$ |
| 31 | $[31, 31, w^3 - 4 w + 1]$ | $\phantom{-}e - 2$ |
| 31 | $[31, 31, -w^2 + 2 w + 3]$ | $\phantom{-}e - 2$ |
| 41 | $[41, 41, 2 w^2 - w - 3]$ | $-e - 1$ |
| 41 | $[41, 41, -w^3 + 3 w^2 + w - 4]$ | $-\frac{3}{2} e + 5$ |
| 49 | $[49, 7, 2 w^3 - 3 w^2 - 5 w + 2]$ | $\phantom{-}e - 6$ |
| 49 | $[49, 7, w^2 + w - 3]$ | $\phantom{-}2 e - 7$ |
| 61 | $[61, 61, 2 w^3 - 3 w^2 - 4 w]$ | $\phantom{-}7$ |
| 61 | $[61, 61, -3 w^3 + 4 w^2 + 7 w - 3]$ | $-3 e + 10$ |
| 79 | $[79, 79, 2 w^3 - 4 w^2 - 3 w + 2]$ | $-2 e - 6$ |
| 79 | $[79, 79, w^3 + w^2 - 3 w - 5]$ | $\phantom{-}2 e + 1$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}4 e - 10$ |
| 89 | $[89, 89, -3 w^3 + 4 w^2 + 5 w - 3]$ | $-2 e + 4$ |
| 89 | $[89, 89, 3 w^3 - 2 w^2 - 7 w]$ | $\phantom{-}2 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $131$ | $[131, 131, -3 w^3 + 2 w^2 + 8 w - 2]$ | $1$ |