Base field 4.4.725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 3x^{2} + x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[251,251,w^{3} - w - 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 2x^{3} - 9x^{2} + 14x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, -w^{3} + 2w^{2} + w - 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} - 3w]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - \frac{3}{2}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{7}{2}e + 2$ |
| 19 | $[19, 19, -w^{3} + 2w + 2]$ | $-2e + 2$ |
| 19 | $[19, 19, 2w^{3} - 3w^{2} - 4w + 2]$ | $-e^{2} + e + 5$ |
| 25 | $[25, 5, 2w^{3} - 2w^{2} - 4w + 1]$ | $-\frac{3}{2}e^{3} + 2e^{2} + 14e - \frac{23}{2}$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}e^{3} - e^{2} - 11e + 6$ |
| 31 | $[31, 31, w^{3} - 4w + 1]$ | $\phantom{-}e^{3} - e^{2} - 11e + 8$ |
| 31 | $[31, 31, -w^{2} + 2w + 3]$ | $-e^{3} + e^{2} + 9e - 4$ |
| 41 | $[41, 41, 2w^{2} - w - 3]$ | $\phantom{-}0$ |
| 41 | $[41, 41, -w^{3} + 3w^{2} + w - 4]$ | $-e^{3} + e^{2} + 12e - 9$ |
| 49 | $[49, 7, 2w^{3} - 3w^{2} - 5w + 2]$ | $\phantom{-}e^{3} - 2e^{2} - 10e + 11$ |
| 49 | $[49, 7, w^{2} + w - 3]$ | $-2e^{3} + 3e^{2} + 21e - 13$ |
| 61 | $[61, 61, 2w^{3} - 3w^{2} - 4w]$ | $\phantom{-}e^{3} - 2e^{2} - 11e + 14$ |
| 61 | $[61, 61, -3w^{3} + 4w^{2} + 7w - 3]$ | $-\frac{1}{2}e^{3} + 2e^{2} + 4e - \frac{17}{2}$ |
| 79 | $[79, 79, 2w^{3} - 4w^{2} - 3w + 2]$ | $-e^{3} + 7e + 2$ |
| 79 | $[79, 79, w^{3} + w^{2} - 3w - 5]$ | $\phantom{-}\frac{7}{2}e^{3} - 4e^{2} - 32e + \frac{43}{2}$ |
| 81 | $[81, 3, -3]$ | $-e^{2} - e + 7$ |
| 89 | $[89, 89, -3w^{3} + 4w^{2} + 5w - 3]$ | $\phantom{-}2e^{3} - 4e^{2} - 19e + 21$ |
| 89 | $[89, 89, 3w^{3} - 2w^{2} - 7w]$ | $\phantom{-}3e^{3} - 5e^{2} - 27e + 24$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $251$ | $[251,251,w^{3} - w - 4]$ | $1$ |