Base field 3.3.1304.1
Generator \(w\), with minimal polynomial \(x^{3} - 11x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, 2w^{2} - 21]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $35$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + 2x^{6} - 8x^{5} - 14x^{4} + 16x^{3} + 26x^{2} - 5x - 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ | $\phantom{-}\frac{2}{3}e^{6} + \frac{2}{3}e^{5} - \frac{17}{3}e^{4} - \frac{10}{3}e^{3} + \frac{35}{3}e^{2} + 4e - 4$ |
| 3 | $[3, 3, -w^{2} + 3w + 1]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{1}{3}e^{4} - \frac{7}{3}e^{3} - \frac{2}{3}e^{2} + \frac{10}{3}e - 1$ |
| 9 | $[9, 3, w^{2} + w - 7]$ | $\phantom{-}e^{6} + \frac{1}{3}e^{5} - \frac{29}{3}e^{4} - \frac{1}{3}e^{3} + \frac{67}{3}e^{2} - \frac{2}{3}e - 10$ |
| 11 | $[11, 11, 2w^{2} - 21]$ | $-1$ |
| 17 | $[17, 17, -\frac{1}{2}w^{2} + \frac{5}{2}w]$ | $-e^{6} - e^{5} + 9e^{4} + 4e^{3} - 23e^{2} - e + 14$ |
| 19 | $[19, 19, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ | $\phantom{-}e^{5} + e^{4} - 7e^{3} - 4e^{2} + 9e + 4$ |
| 37 | $[37, 37, w^{2} - w - 13]$ | $-2e^{6} - \frac{5}{3}e^{5} + \frac{52}{3}e^{4} + \frac{20}{3}e^{3} - \frac{107}{3}e^{2} - \frac{14}{3}e + 15$ |
| 37 | $[37, 37, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ | $\phantom{-}\frac{1}{3}e^{6} + e^{5} - \frac{8}{3}e^{4} - \frac{19}{3}e^{3} + 7e^{2} + \frac{17}{3}e - 6$ |
| 37 | $[37, 37, \frac{5}{2}w^{2} - \frac{17}{2}w - 2]$ | $-2e^{6} - 3e^{5} + 16e^{4} + 16e^{3} - 33e^{2} - 17e + 9$ |
| 47 | $[47, 47, -\frac{3}{2}w^{2} + \frac{11}{2}w]$ | $\phantom{-}\frac{2}{3}e^{5} - \frac{1}{3}e^{4} - \frac{17}{3}e^{3} + \frac{8}{3}e^{2} + \frac{23}{3}e - 2$ |
| 53 | $[53, 53, w^{2} - w - 7]$ | $\phantom{-}\frac{4}{3}e^{6} + \frac{4}{3}e^{5} - \frac{31}{3}e^{4} - \frac{11}{3}e^{3} + \frac{55}{3}e^{2} - 3e - 4$ |
| 59 | $[59, 59, 2w - 1]$ | $-\frac{7}{3}e^{6} - 3e^{5} + \frac{62}{3}e^{4} + \frac{55}{3}e^{3} - 45e^{2} - \frac{71}{3}e + 14$ |
| 61 | $[61, 61, -\frac{3}{2}w^{2} + \frac{3}{2}w + 20]$ | $-\frac{7}{3}e^{6} - \frac{10}{3}e^{5} + \frac{55}{3}e^{4} + \frac{50}{3}e^{3} - \frac{103}{3}e^{2} - 15e + 7$ |
| 67 | $[67, 67, w^{2} - 3w - 3]$ | $-2e^{6} - \frac{7}{3}e^{5} + \frac{56}{3}e^{4} + \frac{46}{3}e^{3} - \frac{133}{3}e^{2} - \frac{64}{3}e + 17$ |
| 71 | $[71, 71, w^{2} - w - 1]$ | $\phantom{-}\frac{1}{3}e^{6} + e^{5} - \frac{5}{3}e^{4} - \frac{22}{3}e^{3} + \frac{47}{3}e$ |
| 73 | $[73, 73, 3w^{2} - w - 33]$ | $-\frac{2}{3}e^{6} - \frac{4}{3}e^{5} + 7e^{4} + 11e^{3} - \frac{70}{3}e^{2} - \frac{59}{3}e + 15$ |
| 79 | $[79, 79, w^{2} - w - 11]$ | $-4e^{6} - 4e^{5} + 33e^{4} + 18e^{3} - 65e^{2} - 17e + 24$ |
| 79 | $[79, 79, w^{2} - 3w + 1]$ | $-\frac{1}{3}e^{6} - \frac{2}{3}e^{5} + \frac{28}{3}e^{2} + \frac{23}{3}e - 12$ |
| 79 | $[79, 79, -2w - 5]$ | $-e^{6} - \frac{2}{3}e^{5} + \frac{25}{3}e^{4} + \frac{8}{3}e^{3} - \frac{44}{3}e^{2} - \frac{20}{3}e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, 2w^{2} - 21]$ | $1$ |