Base field 3.3.257.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[49, 7, 2w^{2} - w - 5]$ |
| 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:
| \(x^{4} + 4x^{3} + x^{2} - 7x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e^{3} + 3e^{2} - 2e - 6$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e^{2} + e - 4$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}e^{3} + 2e^{2} - 3e - 3$ |
| 9 | $[9, 3, -w^{2} + w + 4]$ | $-e^{3} - 4e^{2} + 6$ |
| 19 | $[19, 19, w^{2} + w - 4]$ | $-3e^{3} - 8e^{2} + 6e + 12$ |
| 25 | $[25, 5, -w^{2} + 2w + 2]$ | $-3e^{3} - 9e^{2} + 5e + 10$ |
| 37 | $[37, 37, 2w + 1]$ | $\phantom{-}2e^{3} + 5e^{2} - 6e - 14$ |
| 41 | $[41, 41, -2w^{2} - w + 7]$ | $\phantom{-}3e^{2} + 8e - 6$ |
| 43 | $[43, 43, -2w^{2} + 5]$ | $-4e^{3} - 10e^{2} + 7e + 8$ |
| 47 | $[47, 47, 3w - 4]$ | $\phantom{-}3e^{3} + 9e^{2} - 8e - 16$ |
| 49 | $[49, 7, 2w^{2} - w - 5]$ | $-1$ |
| 53 | $[53, 53, -2w^{2} + 2w + 7]$ | $-e^{3} - 2e^{2} + 2e + 2$ |
| 61 | $[61, 61, -w^{2} - 3w + 4]$ | $\phantom{-}e^{2} + e - 6$ |
| 61 | $[61, 61, 3w^{2} - w - 10]$ | $\phantom{-}6e^{3} + 18e^{2} - 11e - 26$ |
| 61 | $[61, 61, w^{2} - 2w - 4]$ | $\phantom{-}e^{3} - 7e - 2$ |
| 67 | $[67, 67, 2w^{2} - w - 4]$ | $-e^{3} - 3e^{2} + 5e + 8$ |
| 67 | $[67, 67, 2w^{2} - w - 2]$ | $-3e^{3} - 7e^{2} + 13e + 16$ |
| 67 | $[67, 67, w^{2} + 2w - 5]$ | $\phantom{-}3e^{3} + 6e^{2} - 9e - 8$ |
| 71 | $[71, 71, -2w^{2} - w + 10]$ | $-e^{2} + 4e + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $49$ | $[49, 7, 2w^{2} - w - 5]$ | $1$ |