Base field 3.3.985.1
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: | $[17, 17, -w - 3]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 48x^{8} + 785x^{6} - 4916x^{4} + 9216x^{2} - 2048\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $-\frac{107}{12832}e^{8} + \frac{106}{401}e^{6} - \frac{31227}{12832}e^{4} + \frac{22339}{3208}e^{2} - \frac{1980}{401}$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w + 2]$ | $-\frac{47}{51328}e^{9} + \frac{175}{6416}e^{7} - \frac{9759}{51328}e^{5} - \frac{4691}{12832}e^{3} + \frac{7199}{1604}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{95}{25664}e^{8} - \frac{147}{1604}e^{6} + \frac{11535}{25664}e^{4} - \frac{91}{6416}e^{2} + \frac{1235}{401}$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{329}{102656}e^{9} - \frac{813}{6416}e^{7} + \frac{170969}{102656}e^{5} - \frac{211773}{25664}e^{3} + \frac{9557}{802}e$ |
| 17 | $[17, 17, -w - 3]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{127}{51328}e^{9} - \frac{507}{6416}e^{7} + \frac{38383}{51328}e^{5} - \frac{31349}{12832}e^{3} + \frac{4505}{1604}e$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $\phantom{-}\frac{101}{25664}e^{9} - \frac{1119}{6416}e^{7} + \frac{66293}{25664}e^{5} - \frac{22553}{1604}e^{3} + \frac{30515}{1604}e$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{91}{102656}e^{9} + \frac{259}{6416}e^{7} - \frac{69131}{102656}e^{5} + \frac{122599}{25664}e^{3} - \frac{7609}{802}e$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}\frac{5}{1604}e^{8} - \frac{83}{802}e^{6} + \frac{1789}{1604}e^{4} - \frac{3703}{802}e^{2} + \frac{238}{401}$ |
| 29 | $[29, 29, w^{2} - w - 8]$ | $-\frac{333}{25664}e^{8} + \frac{701}{1604}e^{6} - \frac{113373}{25664}e^{4} + \frac{89265}{6416}e^{2} - \frac{2324}{401}$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}\frac{335}{102656}e^{9} - \frac{523}{3208}e^{7} + \frac{277055}{102656}e^{5} - \frac{411367}{25664}e^{3} + \frac{35633}{1604}e$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}\frac{5}{3208}e^{9} - \frac{83}{1604}e^{7} + \frac{1789}{3208}e^{5} - \frac{4505}{1604}e^{3} + \frac{3728}{401}e$ |
| 31 | $[31, 31, w^{2} - 2]$ | $-\frac{351}{102656}e^{9} + \frac{999}{6416}e^{7} - \frac{251983}{102656}e^{5} + \frac{384891}{25664}e^{3} - \frac{19725}{802}e$ |
| 37 | $[37, 37, 2w - 5]$ | $\phantom{-}\frac{25}{102656}e^{9} - \frac{51}{3208}e^{7} + \frac{31401}{102656}e^{5} - \frac{41137}{25664}e^{3} - \frac{3685}{1604}e$ |
| 43 | $[43, 43, w^{2} - 2w - 5]$ | $\phantom{-}\frac{3}{3208}e^{8} - \frac{65}{802}e^{6} + \frac{4923}{3208}e^{4} - \frac{2781}{401}e^{2} + \frac{1114}{401}$ |
| 47 | $[47, 47, w^{2} - 3w - 2]$ | $\phantom{-}\frac{15}{25664}e^{8} + \frac{19}{1604}e^{6} - \frac{17089}{25664}e^{4} + \frac{35949}{6416}e^{2} - \frac{2612}{401}$ |
| 49 | $[49, 7, w^{2} + w - 4]$ | $-\frac{113}{102656}e^{9} + \frac{11}{1604}e^{7} + \frac{55167}{102656}e^{5} - \frac{167839}{25664}e^{3} + \frac{29007}{1604}e$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $-\frac{199}{25664}e^{8} + \frac{443}{1604}e^{6} - \frac{79543}{25664}e^{4} + \frac{80627}{6416}e^{2} - \frac{4592}{401}$ |
| 71 | $[71, 71, w - 5]$ | $-\frac{55}{12832}e^{8} + \frac{32}{401}e^{6} + \frac{2777}{12832}e^{4} - \frac{17929}{3208}e^{2} + \frac{4986}{401}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w - 3]$ | $-1$ |