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: | $[41, 41, -2w^{2} - w + 7]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} - 12x^{4} + 38x^{2} - 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $-\frac{1}{4}e^{5} + 2e^{3} - \frac{3}{2}e$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + 9e$ |
| 8 | $[8, 2, 2]$ | $-e^{2} + 5$ |
| 9 | $[9, 3, -w^{2} + w + 4]$ | $-\frac{1}{4}e^{5} + 3e^{3} - \frac{13}{2}e$ |
| 19 | $[19, 19, w^{2} + w - 4]$ | $\phantom{-}e^{4} - 8e^{2} + 12$ |
| 25 | $[25, 5, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{1}{4}e^{5} - 2e^{3} - \frac{1}{2}e$ |
| 37 | $[37, 37, 2w + 1]$ | $\phantom{-}\frac{1}{4}e^{5} - 2e^{3} + \frac{5}{2}e$ |
| 41 | $[41, 41, -2w^{2} - w + 7]$ | $\phantom{-}1$ |
| 43 | $[43, 43, -2w^{2} + 5]$ | $-\frac{1}{2}e^{5} + 4e^{3} - 5e$ |
| 47 | $[47, 47, 3w - 4]$ | $\phantom{-}e^{4} - 12e^{2} + 24$ |
| 49 | $[49, 7, 2w^{2} - w - 5]$ | $\phantom{-}\frac{3}{4}e^{5} - 7e^{3} + \frac{25}{2}e$ |
| 53 | $[53, 53, -2w^{2} + 2w + 7]$ | $-\frac{7}{4}e^{5} + 17e^{3} - \frac{61}{2}e$ |
| 61 | $[61, 61, -w^{2} - 3w + 4]$ | $-e^{4} + 11e^{2} - 18$ |
| 61 | $[61, 61, 3w^{2} - w - 10]$ | $-\frac{1}{4}e^{5} + 3e^{3} - \frac{17}{2}e$ |
| 61 | $[61, 61, w^{2} - 2w - 4]$ | $\phantom{-}\frac{1}{4}e^{5} - 3e^{3} + \frac{9}{2}e$ |
| 67 | $[67, 67, 2w^{2} - w - 4]$ | $-\frac{1}{2}e^{5} + 4e^{3} - 4e$ |
| 67 | $[67, 67, 2w^{2} - w - 2]$ | $-3e$ |
| 67 | $[67, 67, w^{2} + 2w - 5]$ | $\phantom{-}2e^{4} - 17e^{2} + 28$ |
| 71 | $[71, 71, -2w^{2} - w + 10]$ | $-2e^{4} + 21e^{2} - 32$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, -2w^{2} - w + 7]$ | $-1$ |