Base field 4.4.16448.2
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 7 x^2 + 8 x + 14\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[14, 14, w]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^3 - 3 w^2 - 3 w + 10]$ | $\phantom{-}1$ |
| 2 | $[2, 2, w^3 - 6 w - 5]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^3 + 3 w^2 + 2 w - 7]$ | $-1$ |
| 7 | $[7, 7, -w^3 + 5 w + 3]$ | $-2 e - 1$ |
| 31 | $[31, 31, -w^3 + 2 w^2 + 3 w - 5]$ | $\phantom{-}2 e - 5$ |
| 31 | $[31, 31, -w^2 - w + 1]$ | $\phantom{-}3 e$ |
| 31 | $[31, 31, -w^2 + 3 w - 1]$ | $\phantom{-}2 e - 1$ |
| 31 | $[31, 31, -w^3 + w^2 + 4 w + 1]$ | $-5 e - 1$ |
| 41 | $[41, 41, -w^3 + 3 w^2 + 2 w - 9]$ | $\phantom{-}e + 4$ |
| 41 | $[41, 41, w^3 + w^2 - 8 w - 11]$ | $\phantom{-}2 e + 1$ |
| 47 | $[47, 47, w^3 - w^2 - 4 w + 1]$ | $-6 e + 1$ |
| 47 | $[47, 47, w^3 - 2 w^2 - 3 w + 3]$ | $\phantom{-}4 e - 4$ |
| 49 | $[49, 7, 2 w^2 - 2 w - 9]$ | $\phantom{-}4 e + 1$ |
| 71 | $[71, 71, 5 w^3 - 16 w^2 - 17 w + 61]$ | $-6 e - 4$ |
| 71 | $[71, 71, -2 w^3 - 2 w^2 + 10 w + 13]$ | $\phantom{-}3 e - 13$ |
| 73 | $[73, 73, 3 w^3 + w^2 - 18 w - 17]$ | $-3 e - 6$ |
| 73 | $[73, 73, w^3 - 5 w - 1]$ | $\phantom{-}2 e - 9$ |
| 73 | $[73, 73, w^3 - 7 w - 3]$ | $\phantom{-}3 e - 9$ |
| 73 | $[73, 73, -3 w^3 + 10 w^2 + 7 w - 31]$ | $\phantom{-}3$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}2 e - 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^3 - 3 w^2 - 3 w + 10]$ | $-1$ |
| $7$ | $[7, 7, -w^3 + 3 w^2 + 2 w - 7]$ | $1$ |