Base field 6.6.1279733.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[41, 41, -w^{5} + w^{4} + 4w^{3} - w^{2} - 3w - 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 28x^{4} + 212x^{2} - 432\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 6w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{4} + w^{3} + 4w^{2} - w - 1]$ | $-e$ |
| 13 | $[13, 13, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 3w - 3]$ | $-e^{2} + 10$ |
| 29 | $[29, 29, -w^{4} + w^{3} + 4w^{2} - 3w - 2]$ | $-\frac{1}{12}e^{5} + \frac{11}{6}e^{3} - \frac{20}{3}e$ |
| 29 | $[29, 29, w^{4} - 5w^{2} - 2w + 4]$ | $\phantom{-}\frac{1}{12}e^{5} - \frac{11}{6}e^{3} + \frac{20}{3}e$ |
| 29 | $[29, 29, -w^{4} + w^{3} + 3w^{2} - w + 2]$ | $\phantom{-}\frac{1}{12}e^{5} - \frac{11}{6}e^{3} + \frac{23}{3}e$ |
| 29 | $[29, 29, -w^{2} + w + 1]$ | $-\frac{1}{12}e^{5} + \frac{11}{6}e^{3} - \frac{23}{3}e$ |
| 41 | $[41, 41, -w^{5} + w^{4} + 4w^{3} - w^{2} - 3w - 1]$ | $-1$ |
| 43 | $[43, 43, 2w^{3} - 2w^{2} - 7w + 3]$ | $-\frac{1}{6}e^{5} + \frac{11}{3}e^{3} - \frac{49}{3}e$ |
| 43 | $[43, 43, w^{3} - w^{2} - 2w + 1]$ | $\phantom{-}\frac{1}{6}e^{5} - \frac{11}{3}e^{3} + \frac{49}{3}e$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}e^{2} - 11$ |
| 71 | $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ | $\phantom{-}\frac{1}{2}e^{4} - 10e^{2} + 36$ |
| 71 | $[71, 71, w^{5} - 2w^{4} - 2w^{3} + 5w^{2} - 3w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - 10e^{2} + 36$ |
| 83 | $[83, 83, -2w^{4} + 3w^{3} + 6w^{2} - 7w + 2]$ | $-3e$ |
| 83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 2w + 3]$ | $\phantom{-}3e$ |
| 83 | $[83, 83, -w^{5} + 3w^{4} + w^{3} - 9w^{2} + 5w + 3]$ | $-\frac{1}{2}e^{4} + 12e^{2} - 48$ |
| 83 | $[83, 83, w^{5} - 7w^{3} + 10w - 1]$ | $-\frac{1}{2}e^{4} + 12e^{2} - 48$ |
| 97 | $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 1]$ | $-\frac{1}{4}e^{5} + \frac{11}{2}e^{3} - 24e$ |
| 97 | $[97, 97, w^{5} - 5w^{3} - w^{2} + 3w - 3]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{11}{2}e^{3} + 24e$ |
| 113 | $[113, 113, w^{4} - w^{3} - 4w^{2} + w + 4]$ | $-\frac{1}{4}e^{5} + \frac{11}{2}e^{3} - 21e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, -w^{5} + w^{4} + 4w^{3} - w^{2} - 3w - 1]$ | $1$ |