Base field 4.4.2624.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 3x^{2} + 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[49, 7, 2w^{3} - 4w^{2} - 4w + 1]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 2x^{2} - 9x + 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{3} + 3w^{2} + w - 3]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w^{2} + w + 2]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} - 3]$ | $\phantom{-}0$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w]$ | $\phantom{-}0$ |
| 25 | $[25, 5, -w^{3} + 3w^{2} + 2w - 2]$ | $-2e$ |
| 25 | $[25, 5, -2w^{3} + 4w^{2} + 5w - 1]$ | $-2e$ |
| 41 | $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ | $-2e^{2} + 2e + 10$ |
| 47 | $[47, 47, -2w^{3} + 5w^{2} + 4w - 4]$ | $-2e + 4$ |
| 47 | $[47, 47, 2w^{3} - 4w^{2} - 5w]$ | $-2e + 4$ |
| 49 | $[49, 7, w^{2} - 4w - 1]$ | $\phantom{-}2e + 4$ |
| 71 | $[71, 71, 2w - 3]$ | $\phantom{-}2e^{2} - 4e - 12$ |
| 71 | $[71, 71, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}2e^{2} - 4e - 12$ |
| 73 | $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ | $-2e^{2} + 4e + 14$ |
| 73 | $[73, 73, 2w^{3} - 5w^{2} - 5w + 4]$ | $-2e^{2} + 4e + 14$ |
| 73 | $[73, 73, -w^{3} + 3w^{2} - 5]$ | $\phantom{-}2e - 8$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}2e - 8$ |
| 79 | $[79, 79, 2w^{3} - 3w^{2} - 6w + 2]$ | $-2e$ |
| 79 | $[79, 79, 2w^{3} - 3w^{2} - 5w]$ | $-2e$ |
| 81 | $[81, 3, -3]$ | $-2e^{2} + 2e + 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w^{3} + 3w^{2} + w - 3]$ | $-1$ |
| $7$ | $[7, 7, -w^{2} + w + 2]$ | $-1$ |