Base field 3.3.761.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, -w^{2} + 2w + 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 2x^{4} - 7x^{3} - 8x^{2} + 8x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 9e + 6$ |
| 8 | $[8, 2, 2]$ | $-\frac{4}{3}e^{4} - \frac{10}{3}e^{3} + \frac{23}{3}e^{2} + 14e - \frac{14}{3}$ |
| 9 | $[9, 3, -w^{2} + 2w + 4]$ | $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 8e + 1$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $-1$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-e^{4} - 2e^{3} + 6e^{2} + 7e - 4$ |
| 19 | $[19, 19, w + 3]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{4}{3}e^{3} - \frac{5}{3}e^{2} - 5e + \frac{5}{3}$ |
| 19 | $[19, 19, -w^{2} + 2w + 5]$ | $\phantom{-}e^{2} + 2e - 3$ |
| 19 | $[19, 19, -w^{2} + 3w + 2]$ | $-\frac{4}{3}e^{4} - \frac{7}{3}e^{3} + \frac{26}{3}e^{2} + 8e - \frac{29}{3}$ |
| 23 | $[23, 23, w^{2} - w - 3]$ | $-\frac{5}{3}e^{4} - \frac{11}{3}e^{3} + \frac{31}{3}e^{2} + 16e - \frac{25}{3}$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}2e^{4} + 4e^{3} - 13e^{2} - 18e + 6$ |
| 23 | $[23, 23, -w + 4]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{4}{3}e^{3} + \frac{1}{3}e^{2} - 6e - \frac{16}{3}$ |
| 31 | $[31, 31, w^{2} - 5]$ | $\phantom{-}\frac{4}{3}e^{4} + \frac{13}{3}e^{3} - \frac{23}{3}e^{2} - 21e + \frac{20}{3}$ |
| 43 | $[43, 43, w^{2} - 3w - 3]$ | $\phantom{-}e^{4} + 3e^{3} - 4e^{2} - 14e$ |
| 49 | $[49, 7, w^{2} - 6]$ | $-\frac{7}{3}e^{4} - \frac{16}{3}e^{3} + \frac{41}{3}e^{2} + 19e - \frac{35}{3}$ |
| 53 | $[53, 53, 2w - 5]$ | $-\frac{10}{3}e^{4} - \frac{25}{3}e^{3} + \frac{59}{3}e^{2} + 38e - \frac{41}{3}$ |
| 61 | $[61, 61, 2w^{2} - 2w - 9]$ | $\phantom{-}2e^{4} + 4e^{3} - 13e^{2} - 13e + 13$ |
| 71 | $[71, 71, 2w - 3]$ | $\phantom{-}\frac{4}{3}e^{4} + \frac{7}{3}e^{3} - \frac{32}{3}e^{2} - 11e + \frac{20}{3}$ |
| 73 | $[73, 73, 2w^{2} - 5w - 5]$ | $-5e^{4} - 13e^{3} + 29e^{2} + 54e - 24$ |
| 83 | $[83, 83, w^{2} - w - 9]$ | $-\frac{1}{3}e^{4} + \frac{2}{3}e^{3} + \frac{8}{3}e^{2} - 5e - \frac{2}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{2} + 2w + 2]$ | $1$ |