Base field 3.3.229.1
Generator \(w\), with minimal polynomial \(x^{3} - 4x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[49, 7, 2w^{2} - w - 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 3x^{3} - x^{2} - 6x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} + w + 3]$ | $\phantom{-}e^{2} + e - 3$ |
| 7 | $[7, 7, w^{2} - 2]$ | $-e - 3$ |
| 13 | $[13, 13, -w^{2} + 2w + 2]$ | $-e^{2} - e$ |
| 23 | $[23, 23, -2w + 1]$ | $\phantom{-}2e^{3} + 3e^{2} - 5e - 4$ |
| 27 | $[27, 3, 3]$ | $-4e^{3} - 8e^{2} + 9e + 11$ |
| 29 | $[29, 29, -2w + 3]$ | $\phantom{-}4e^{3} + 5e^{2} - 12e - 7$ |
| 31 | $[31, 31, -2w^{2} + 2w + 3]$ | $\phantom{-}e^{3} - e^{2} - 5e + 5$ |
| 37 | $[37, 37, 4w^{2} - 2w - 13]$ | $\phantom{-}2e^{2} + 5e - 1$ |
| 37 | $[37, 37, -2w^{2} + 5]$ | $-2e^{3} - 7e^{2} + 2e + 9$ |
| 37 | $[37, 37, 2w^{2} - w - 10]$ | $-e^{2} - 3e - 2$ |
| 41 | $[41, 41, w^{2} - 2w - 4]$ | $-5e^{3} - 9e^{2} + 10e + 6$ |
| 47 | $[47, 47, w - 4]$ | $\phantom{-}2e^{3} + 6e^{2} - e - 11$ |
| 49 | $[49, 7, 2w^{2} - w - 4]$ | $-1$ |
| 53 | $[53, 53, 2w^{2} - 2w - 7]$ | $\phantom{-}e^{3} + 6e^{2} + e - 14$ |
| 53 | $[53, 53, 3w^{2} - 2w - 8]$ | $\phantom{-}5e^{3} + 9e^{2} - 12e - 12$ |
| 53 | $[53, 53, 2w + 5]$ | $-e^{3} - 2e^{2} + 9e + 8$ |
| 59 | $[59, 59, 2w^{2} - 2w - 9]$ | $-6e^{3} - 12e^{2} + 10e + 12$ |
| 67 | $[67, 67, 2w^{2} - 3]$ | $\phantom{-}4e^{3} + 7e^{2} - 12e - 11$ |
| 73 | $[73, 73, 2w^{2} + w - 8]$ | $\phantom{-}e^{3} + 7e^{2} + 6e - 16$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $49$ | $[49, 7, 2w^{2} - w - 4]$ | $1$ |