Base field 3.3.1944.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 6\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[3, 3, w^{2} - w - 9]$ |
| Dimension: | $10$ |
| 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:
| \(x^{10} - x^{9} - 16x^{8} + 15x^{7} + 85x^{6} - 67x^{5} - 174x^{4} + 93x^{3} + 112x^{2} - 16x - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 2w + 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-\frac{1}{8}e^{9} + \frac{7}{4}e^{7} - \frac{1}{8}e^{6} - \frac{29}{4}e^{5} + \frac{7}{8}e^{4} + \frac{65}{8}e^{3} - \frac{7}{4}e^{2} + \frac{3}{2}e$ |
| 3 | $[3, 3, w^{2} - w - 9]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w^{2} - w - 7]$ | $\phantom{-}\frac{3}{4}e^{8} + \frac{1}{2}e^{7} - \frac{21}{2}e^{6} - \frac{21}{4}e^{5} + 45e^{4} + \frac{55}{4}e^{3} - \frac{241}{4}e^{2} - e + 13$ |
| 11 | $[11, 11, w^{2} - w - 1]$ | $\phantom{-}\frac{1}{2}e^{8} - 7e^{6} + \frac{1}{2}e^{5} + 30e^{4} - \frac{7}{2}e^{3} - \frac{83}{2}e^{2} + 7e + 10$ |
| 13 | $[13, 13, -2w - 1]$ | $\phantom{-}\frac{1}{2}e^{8} + \frac{1}{2}e^{7} - \frac{13}{2}e^{6} - 6e^{5} + 24e^{4} + \frac{41}{2}e^{3} - 22e^{2} - 15e + 2$ |
| 17 | $[17, 17, -2w^{2} + 6w + 5]$ | $-\frac{3}{4}e^{9} + \frac{1}{2}e^{8} + 11e^{7} - \frac{33}{4}e^{6} - \frac{101}{2}e^{5} + \frac{161}{4}e^{4} + \frac{313}{4}e^{3} - \frac{125}{2}e^{2} - 24e + 10$ |
| 31 | $[31, 31, -2w^{2} + 2w + 19]$ | $-\frac{3}{2}e^{8} - e^{7} + 21e^{6} + \frac{23}{2}e^{5} - 90e^{4} - \frac{75}{2}e^{3} + \frac{243}{2}e^{2} + 23e - 23$ |
| 37 | $[37, 37, 2w^{2} - 13]$ | $\phantom{-}\frac{1}{2}e^{9} - e^{8} - 8e^{7} + \frac{29}{2}e^{6} + 41e^{5} - \frac{127}{2}e^{4} - \frac{147}{2}e^{3} + 87e^{2} + 26e - 13$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{1}{4}e^{9} - \frac{1}{2}e^{8} + 3e^{7} + \frac{25}{4}e^{6} - \frac{19}{2}e^{5} - \frac{93}{4}e^{4} + \frac{19}{4}e^{3} + \frac{47}{2}e^{2} - 2$ |
| 43 | $[43, 43, 2w^{2} - 2w - 17]$ | $\phantom{-}\frac{5}{4}e^{8} + \frac{1}{2}e^{7} - \frac{35}{2}e^{6} - \frac{19}{4}e^{5} + 75e^{4} + \frac{49}{4}e^{3} - \frac{407}{4}e^{2} - 4e + 23$ |
| 43 | $[43, 43, -2w + 7]$ | $\phantom{-}e^{8} - 14e^{6} + e^{5} + 60e^{4} - 6e^{3} - 82e^{2} + 9e + 19$ |
| 43 | $[43, 43, 12w^{2} - 8w - 101]$ | $-e^{9} - \frac{1}{4}e^{8} + \frac{29}{2}e^{7} + \frac{3}{2}e^{6} - \frac{265}{4}e^{5} + 3e^{4} + \frac{407}{4}e^{3} - \frac{93}{4}e^{2} - 29e + 7$ |
| 49 | $[49, 7, w^{2} + w - 1]$ | $-\frac{1}{4}e^{9} + \frac{1}{4}e^{8} + \frac{7}{2}e^{7} - \frac{17}{4}e^{6} - \frac{59}{4}e^{5} + \frac{87}{4}e^{4} + \frac{35}{2}e^{3} - \frac{147}{4}e^{2} + 8e + 11$ |
| 59 | $[59, 59, -w^{2} + w + 11]$ | $\phantom{-}\frac{1}{2}e^{9} - 7e^{7} + \frac{1}{2}e^{6} + 30e^{5} - \frac{7}{2}e^{4} - \frac{83}{2}e^{3} + 11e^{2} + 10e - 12$ |
| 61 | $[61, 61, -w^{2} - w - 1]$ | $-\frac{1}{4}e^{9} - \frac{1}{4}e^{8} + \frac{7}{2}e^{7} + \frac{11}{4}e^{6} - \frac{61}{4}e^{5} - \frac{33}{4}e^{4} + 23e^{3} + \frac{27}{4}e^{2} - 13e - 5$ |
| 79 | $[79, 79, -2w^{2} + 4w + 7]$ | $-\frac{1}{2}e^{9} + 7e^{7} - \frac{3}{2}e^{6} - 30e^{5} + \frac{27}{2}e^{4} + \frac{79}{2}e^{3} - 32e^{2} - 4e + 16$ |
| 83 | $[83, 83, 2w - 1]$ | $\phantom{-}\frac{1}{2}e^{9} - 7e^{7} + \frac{1}{2}e^{6} + 30e^{5} - \frac{5}{2}e^{4} - \frac{81}{2}e^{3} + 2e^{2} + 5e$ |
| 89 | $[89, 89, 5w^{2} - 3w - 43]$ | $-e^{9} + e^{8} + 15e^{7} - 16e^{6} - 71e^{5} + 78e^{4} + 113e^{3} - 123e^{2} - 26e + 20$ |
| 103 | $[103, 103, -2w + 5]$ | $\phantom{-}\frac{1}{2}e^{9} + \frac{1}{4}e^{8} - \frac{13}{2}e^{7} - 3e^{6} + \frac{97}{4}e^{5} + \frac{27}{2}e^{4} - \frac{89}{4}e^{3} - \frac{103}{4}e^{2} - 8e + 15$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w^{2} - w - 9]$ | $-1$ |