Base field 4.4.14013.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 6 x^2 + 6 x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[7, 7, w + 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - 10\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-e$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 1]$ | $-1$ |
| 7 | $[7, 7, -w^3 + 5 w - 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^3 + 5 w + 1]$ | $-2 e$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}5$ |
| 29 | $[29, 29, w^3 + w^2 - 5 w - 1]$ | $\phantom{-}e$ |
| 31 | $[31, 31, -w^3 + 4 w - 1]$ | $-2 e$ |
| 41 | $[41, 41, w^3 - 6 w + 1]$ | $\phantom{-}2 e$ |
| 43 | $[43, 43, w^3 + w^2 - 6 w - 1]$ | $\phantom{-}4 e$ |
| 47 | $[47, 47, -w^3 + 2 w^2 + 5 w - 11]$ | $\phantom{-}8$ |
| 49 | $[49, 7, w^2 + w - 1]$ | $\phantom{-}2 e$ |
| 59 | $[59, 59, w^3 - w^2 - 6 w + 4]$ | $\phantom{-}e$ |
| 59 | $[59, 59, w^2 - w - 4]$ | $\phantom{-}4$ |
| 67 | $[67, 67, 2 w^3 + w^2 - 9 w - 2]$ | $-3 e$ |
| 71 | $[71, 71, -3 w^3 - w^2 + 16 w + 5]$ | $\phantom{-}3 e$ |
| 71 | $[71, 71, 2 w - 1]$ | $-4 e$ |
| 73 | $[73, 73, w^3 - 6 w + 4]$ | $-e$ |
| 83 | $[83, 83, w^3 - w^2 - 3 w + 4]$ | $-4$ |
| 103 | $[103, 103, w^3 + w^2 - 4 w - 5]$ | $-14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w + 1]$ | $1$ |