Base field 6.6.1292517.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - x^{3} + 6x^{2} - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[17, 17, w^{5} - 5w^{3} - 2w^{2} + w + 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - x^{5} - 25x^{4} + 19x^{3} + 133x^{2} - 16x - 104\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{5} + 6w^{3} + w^{2} - 5w - 1]$ | $\phantom{-}e$ |
| 17 | $[17, 17, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 5w + 1]$ | $-\frac{68}{1879}e^{5} + \frac{91}{1879}e^{4} + \frac{1310}{1879}e^{3} - \frac{2343}{1879}e^{2} - \frac{3029}{1879}e + \frac{11922}{1879}$ |
| 17 | $[17, 17, w^{5} - 5w^{3} - 2w^{2} + w + 2]$ | $-1$ |
| 17 | $[17, 17, w^{4} - 5w^{2} - 2w + 1]$ | $\phantom{-}\frac{68}{1879}e^{5} - \frac{91}{1879}e^{4} - \frac{1310}{1879}e^{3} + \frac{2343}{1879}e^{2} + \frac{1150}{1879}e - \frac{4406}{1879}$ |
| 17 | $[17, 17, -w^{5} - w^{4} + 5w^{3} + 7w^{2} - 3]$ | $-\frac{7}{1879}e^{5} + \frac{37}{1879}e^{4} - \frac{252}{1879}e^{3} - \frac{932}{1879}e^{2} + \frac{4137}{1879}e + \frac{8688}{1879}$ |
| 19 | $[19, 19, 2w^{5} - 11w^{3} - 2w^{2} + 7w]$ | $\phantom{-}\frac{289}{3758}e^{5} + \frac{83}{3758}e^{4} - \frac{6507}{3758}e^{3} + \frac{93}{3758}e^{2} + \frac{24617}{3758}e + \frac{502}{1879}$ |
| 19 | $[19, 19, w^{5} - 5w^{3} - w^{2} + 2w - 1]$ | $\phantom{-}\frac{63}{1879}e^{5} - \frac{333}{1879}e^{4} - \frac{1490}{1879}e^{3} + \frac{6509}{1879}e^{2} + \frac{5984}{1879}e - \frac{10548}{1879}$ |
| 37 | $[37, 37, w^{5} - 5w^{3} - 2w^{2} + 2w + 3]$ | $-\frac{31}{3758}e^{5} - \frac{373}{3758}e^{4} + \frac{763}{3758}e^{3} + \frac{7415}{3758}e^{2} - \frac{469}{3758}e - \frac{8142}{1879}$ |
| 37 | $[37, 37, -2w^{5} - w^{4} + 11w^{3} + 8w^{2} - 6w - 2]$ | $-\frac{70}{1879}e^{5} + \frac{370}{1879}e^{4} + \frac{1238}{1879}e^{3} - \frac{7441}{1879}e^{2} + \frac{1911}{1879}e + \frac{19236}{1879}$ |
| 53 | $[53, 53, -w^{5} - w^{4} + 6w^{3} + 5w^{2} - 4w - 1]$ | $\phantom{-}\frac{127}{1879}e^{5} + \frac{134}{1879}e^{4} - \frac{2944}{1879}e^{3} - \frac{3223}{1879}e^{2} + \frac{11377}{1879}e + \frac{14706}{1879}$ |
| 53 | $[53, 53, w^{3} - 4w + 1]$ | $-\frac{209}{1879}e^{5} + \frac{31}{1879}e^{4} + \frac{5629}{1879}e^{3} - \frac{984}{1879}e^{2} - \frac{28680}{1879}e + \frac{3318}{1879}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{225}{1879}e^{5} - \frac{384}{1879}e^{4} - \frac{5053}{1879}e^{3} + \frac{6067}{1879}e^{2} + \frac{21103}{1879}e + \frac{177}{1879}$ |
| 73 | $[73, 73, -3w^{5} + 17w^{3} + 3w^{2} - 12w + 1]$ | $\phantom{-}\frac{54}{1879}e^{5} - \frac{17}{1879}e^{4} - \frac{1814}{1879}e^{3} - \frac{1400}{1879}e^{2} + \frac{13182}{1879}e + \frac{20486}{1879}$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{495}{3758}e^{5} - \frac{469}{3758}e^{4} - \frac{10365}{3758}e^{3} + \frac{6583}{3758}e^{2} + \frac{30643}{3758}e - \frac{2248}{1879}$ |
| 73 | $[73, 73, 2w^{5} + w^{4} - 11w^{3} - 7w^{2} + 5w + 3]$ | $-\frac{143}{3758}e^{5} + \frac{219}{3758}e^{4} + \frac{4247}{3758}e^{3} - \frac{3739}{3758}e^{2} - \frac{35743}{3758}e - \frac{2524}{1879}$ |
| 73 | $[73, 73, 2w^{5} + w^{4} - 11w^{3} - 8w^{2} + 5w + 4]$ | $-\frac{281}{1879}e^{5} + \frac{680}{1879}e^{4} + \frac{6795}{1879}e^{3} - \frac{11644}{1879}e^{2} - \frac{31224}{1879}e + \frac{7320}{1879}$ |
| 107 | $[107, 107, -w^{4} + w^{3} + 5w^{2} - 2w - 3]$ | $\phantom{-}\frac{126}{1879}e^{5} - \frac{666}{1879}e^{4} - \frac{2980}{1879}e^{3} + \frac{14897}{1879}e^{2} + \frac{10089}{1879}e - \frac{36128}{1879}$ |
| 107 | $[107, 107, -3w^{5} - w^{4} + 17w^{3} + 8w^{2} - 11w - 2]$ | $\phantom{-}\frac{101}{1879}e^{5} + \frac{3}{1879}e^{4} - \frac{2001}{1879}e^{3} + \frac{1905}{1879}e^{2} + \frac{2316}{1879}e - \frac{2952}{1879}$ |
| 109 | $[109, 109, w^{4} - 6w^{2} + 5]$ | $-\frac{101}{1879}e^{5} - \frac{3}{1879}e^{4} + \frac{2001}{1879}e^{3} - \frac{26}{1879}e^{2} - \frac{9832}{1879}e - \frac{806}{1879}$ |
| 109 | $[109, 109, -w^{5} + 6w^{3} + w^{2} - 7w + 1]$ | $\phantom{-}\frac{267}{1879}e^{5} - \frac{606}{1879}e^{4} - \frac{5420}{1879}e^{3} + \frac{11659}{1879}e^{2} + \frac{13192}{1879}e - \frac{20008}{1879}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{5} - 5w^{3} - 2w^{2} + w + 2]$ | $1$ |