Base field 6.6.485125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 8x^{3} + 2x^{2} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 2x^{4} - 24x^{3} - 20x^{2} + 48x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}e$ |
| 19 | $[19, 19, -w^{3} + 4w]$ | $\phantom{-}\frac{1}{6}e^{3} - \frac{10}{3}e + \frac{10}{3}$ |
| 19 | $[19, 19, w^{3} - 3w - 1]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{2}{3}e^{3} - \frac{11}{2}e^{2} - \frac{28}{3}e + \frac{22}{3}$ |
| 29 | $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ | $-\frac{1}{6}e^{4} - \frac{1}{2}e^{3} + \frac{10}{3}e^{2} + \frac{20}{3}e$ |
| 29 | $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $-\frac{1}{6}e^{4} - \frac{1}{2}e^{3} + \frac{10}{3}e^{2} + \frac{20}{3}e$ |
| 31 | $[31, 31, -w^{4} + 4w^{2} + w - 3]$ | $-\frac{1}{12}e^{4} - \frac{1}{3}e^{3} + \frac{5}{3}e^{2} + 6e + \frac{4}{3}$ |
| 41 | $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ | $-1$ |
| 49 | $[49, 7, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 11w + 6]$ | $\phantom{-}\frac{1}{12}e^{4} - \frac{13}{6}e^{2} + \frac{8}{3}e + 4$ |
| 59 | $[59, 59, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 7w - 5]$ | $-\frac{1}{2}e^{4} - \frac{4}{3}e^{3} + 11e^{2} + \frac{47}{3}e - \frac{32}{3}$ |
| 59 | $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{7}{6}e^{3} - 11e^{2} - \frac{34}{3}e + \frac{34}{3}$ |
| 59 | $[59, 59, 2w^{5} - 3w^{4} - 9w^{3} + 11w^{2} + 9w - 4]$ | $-\frac{1}{12}e^{4} - \frac{1}{3}e^{3} + \frac{13}{6}e^{2} + 6e - \frac{20}{3}$ |
| 61 | $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ | $-\frac{1}{6}e^{4} - \frac{1}{3}e^{3} + \frac{10}{3}e^{2} + \frac{7}{3}e - \frac{8}{3}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{5}{12}e^{4} + \frac{2}{3}e^{3} - \frac{31}{3}e^{2} - 6e + \frac{49}{3}$ |
| 71 | $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ | $-\frac{1}{3}e^{4} - e^{3} + \frac{20}{3}e^{2} + \frac{37}{3}e - 6$ |
| 79 | $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ | $\phantom{-}\frac{1}{6}e^{4} + \frac{1}{6}e^{3} - \frac{13}{3}e^{2} - 2e + \frac{34}{3}$ |
| 79 | $[79, 79, -w^{4} - w^{3} + 5w^{2} + 4w - 3]$ | $\phantom{-}\frac{1}{12}e^{4} + \frac{1}{3}e^{3} - \frac{7}{6}e^{2} - 4e - \frac{4}{3}$ |
| 79 | $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 8w + 4]$ | $-\frac{1}{12}e^{4} + \frac{13}{6}e^{2} - \frac{8}{3}e$ |
| 81 | $[81, 3, 3w^{5} - 5w^{4} - 14w^{3} + 19w^{2} + 13w - 8]$ | $-\frac{7}{12}e^{4} - \frac{3}{2}e^{3} + \frac{41}{3}e^{2} + \frac{58}{3}e - 20$ |
| 89 | $[89, 89, 2w^{5} - 2w^{4} - 9w^{3} + 6w^{2} + 8w - 1]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{5}{6}e^{3} - \frac{23}{3}e^{2} - 10e + \frac{44}{3}$ |
| 101 | $[101, 101, -w^{4} - w^{3} + 5w^{2} + 3w - 3]$ | $-\frac{7}{12}e^{4} - \frac{4}{3}e^{3} + \frac{41}{3}e^{2} + 16e - \frac{50}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ | $1$ |