Base field 4.4.4352.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 4x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[41,41,-w^{3} + 3w^{2} + 2w - 5]$ |
| Dimension: | $8$ |
| 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:
| \(x^{8} - 28x^{6} + 270x^{4} - 1038x^{2} + 1376\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}\frac{1}{2}e^{6} - 12e^{4} + 88e^{2} - 182$ |
| 7 | $[7, 7, -w^{3} + w^{2} + 5w + 1]$ | $\phantom{-}\frac{1}{4}e^{7} - 6e^{5} + \frac{89}{2}e^{3} - \frac{191}{2}e$ |
| 7 | $[7, 7, -w + 1]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}e^{4} - 14e^{2} + 38$ |
| 23 | $[23, 23, -2w^{3} + 2w^{2} + 9w + 1]$ | $\phantom{-}\frac{1}{4}e^{7} - 6e^{5} + \frac{89}{2}e^{3} - \frac{187}{2}e$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w + 1]$ | $\phantom{-}e^{7} - 25e^{5} + 191e^{3} - 409e$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $\phantom{-}\frac{3}{4}e^{7} - 18e^{5} + \frac{265}{2}e^{3} - \frac{555}{2}e$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 3w + 5]$ | $-\frac{3}{2}e^{7} + 36e^{5} - 265e^{3} + 553e$ |
| 41 | $[41, 41, w^{3} - 3w^{2} - 2w + 7]$ | $-e^{4} + 15e^{2} - 42$ |
| 41 | $[41, 41, w^{3} - 3w^{2} - 2w + 5]$ | $-1$ |
| 49 | $[49, 7, 2w^{3} - 2w^{2} - 8w - 1]$ | $-2e^{6} + 50e^{4} - 383e^{2} + 826$ |
| 71 | $[71, 71, -2w^{3} + 3w^{2} + 8w - 1]$ | $-\frac{7}{4}e^{7} + 43e^{5} - \frac{647}{2}e^{3} + \frac{1377}{2}e$ |
| 71 | $[71, 71, w^{2} - 5]$ | $\phantom{-}\frac{3}{2}e^{7} - 37e^{5} + 279e^{3} - 588e$ |
| 73 | $[73, 73, -3w^{3} + 4w^{2} + 11w - 3]$ | $-e^{6} + 24e^{4} - 176e^{2} + 374$ |
| 73 | $[73, 73, 2w^{3} - w^{2} - 9w - 3]$ | $-3e^{6} + 75e^{4} - 574e^{2} + 1234$ |
| 79 | $[79, 79, 3w^{3} - 4w^{2} - 13w + 3]$ | $\phantom{-}\frac{3}{2}e^{7} - 36e^{5} + 265e^{3} - 553e$ |
| 79 | $[79, 79, w^{2} + w - 3]$ | $-e^{7} + 25e^{5} - 192e^{3} + 416e$ |
| 81 | $[81, 3, -3]$ | $-2e^{6} + 47e^{4} - 340e^{2} + 706$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 3w - 11]$ | $-3e^{6} + 71e^{4} - 517e^{2} + 1078$ |
| 89 | $[89, 89, 3w^{3} - 2w^{2} - 14w - 3]$ | $\phantom{-}e^{6} - 25e^{4} + 193e^{2} - 422$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41,41,-w^{3} + 3w^{2} + 2w - 5]$ | $1$ |