Base field 3.3.756.1
Generator \(w\), with minimal polynomial \(x^{3} - 6x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, -w - 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 3x^{7} - 9x^{6} - 31x^{5} + 12x^{4} + 81x^{3} + 29x^{2} - 33x - 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{3}e^{7} + \frac{1}{2}e^{6} - \frac{7}{2}e^{5} - \frac{13}{3}e^{4} + 9e^{3} + 8e^{2} - \frac{17}{6}e + \frac{1}{2}$ |
| 7 | $[7, 7, -w + 3]$ | $-\frac{17}{6}e^{7} - \frac{9}{2}e^{6} + 32e^{5} + \frac{130}{3}e^{4} - 96e^{3} - \frac{199}{2}e^{2} + \frac{341}{6}e + 21$ |
| 7 | $[7, 7, w - 1]$ | $-\frac{7}{3}e^{7} - 4e^{6} + 26e^{5} + \frac{115}{3}e^{4} - 76e^{3} - 87e^{2} + \frac{121}{3}e + 18$ |
| 11 | $[11, 11, -w - 3]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}\frac{8}{3}e^{7} + \frac{9}{2}e^{6} - \frac{59}{2}e^{5} - \frac{131}{3}e^{4} + 84e^{3} + 101e^{2} - \frac{241}{6}e - \frac{39}{2}$ |
| 19 | $[19, 19, -w^{2} - w + 1]$ | $-\frac{7}{3}e^{7} - 4e^{6} + 26e^{5} + \frac{115}{3}e^{4} - 76e^{3} - 85e^{2} + \frac{121}{3}e + 12$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{13}{2}e^{7} - \frac{21}{2}e^{6} + 73e^{5} + 100e^{4} - 217e^{3} - \frac{447}{2}e^{2} + \frac{251}{2}e + 39$ |
| 29 | $[29, 29, 2w + 3]$ | $\phantom{-}\frac{1}{2}e^{7} + \frac{1}{2}e^{6} - 6e^{5} - 4e^{4} + 20e^{3} + \frac{11}{2}e^{2} - \frac{29}{2}e + 3$ |
| 31 | $[31, 31, 2w^{2} - 2w - 9]$ | $\phantom{-}e^{7} + e^{6} - 12e^{5} - 9e^{4} + 40e^{3} + 18e^{2} - 31e + 2$ |
| 53 | $[53, 53, -w^{2} - 1]$ | $\phantom{-}4e^{7} + 6e^{6} - 46e^{5} - 57e^{4} + 142e^{3} + 126e^{2} - 90e - 21$ |
| 61 | $[61, 61, 2w - 3]$ | $-\frac{4}{3}e^{7} - 3e^{6} + 14e^{5} + \frac{88}{3}e^{4} - 36e^{3} - 67e^{2} + \frac{34}{3}e + 18$ |
| 67 | $[67, 67, w^{2} - 2w - 5]$ | $\phantom{-}\frac{14}{3}e^{7} + \frac{15}{2}e^{6} - \frac{105}{2}e^{5} - \frac{215}{3}e^{4} + 157e^{3} + 160e^{2} - \frac{577}{6}e - \frac{57}{2}$ |
| 67 | $[67, 67, -w^{2} + w + 9]$ | $-\frac{53}{6}e^{7} - \frac{29}{2}e^{6} + 99e^{5} + \frac{418}{3}e^{4} - 292e^{3} - \frac{635}{2}e^{2} + \frac{965}{6}e + 63$ |
| 67 | $[67, 67, -w^{2} + 3w + 3]$ | $\phantom{-}\frac{2}{3}e^{7} + e^{6} - 8e^{5} - \frac{29}{3}e^{4} + 27e^{3} + 23e^{2} - \frac{59}{3}e - 9$ |
| 71 | $[71, 71, w^{2} + w - 7]$ | $\phantom{-}4e^{7} + 6e^{6} - 46e^{5} - 57e^{4} + 143e^{3} + 128e^{2} - 97e - 27$ |
| 73 | $[73, 73, -2w^{2} + 3w + 7]$ | $-\frac{71}{6}e^{7} - \frac{37}{2}e^{6} + 133e^{5} + \frac{526}{3}e^{4} - 397e^{3} - \frac{781}{2}e^{2} + \frac{1421}{6}e + 72$ |
| 89 | $[89, 89, w^{2} - 2w - 7]$ | $-7e^{7} - 12e^{6} + 78e^{5} + 116e^{4} - 226e^{3} - 266e^{2} + 113e + 54$ |
| 89 | $[89, 89, -2w^{2} + 1]$ | $\phantom{-}6e^{7} + 10e^{6} - 68e^{5} - 96e^{4} + 207e^{3} + 216e^{2} - 131e - 42$ |
| 89 | $[89, 89, -3w^{2} + 19]$ | $-\frac{11}{2}e^{7} - \frac{19}{2}e^{6} + 61e^{5} + 92e^{4} - 176e^{3} - \frac{425}{2}e^{2} + \frac{179}{2}e + 45$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w - 3]$ | $-1$ |