Base field 6.6.1416125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 9x^{3} + 6x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 3]$ |
| Dimension: | $9$ |
| 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:
| \(x^{9} - 6x^{8} - 8x^{7} + 88x^{6} - 44x^{5} - 263x^{4} + 64x^{3} + 308x^{2} + 144x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{4} + 2w^{3} + 3w^{2} - 5w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $-\frac{93}{284}e^{8} + \frac{617}{284}e^{7} + \frac{153}{142}e^{6} - \frac{2043}{71}e^{5} + \frac{2484}{71}e^{4} + \frac{15343}{284}e^{3} - \frac{17689}{284}e^{2} - \frac{2954}{71}e - \frac{28}{71}$ |
| 19 | $[19, 19, -w^{3} + 4w]$ | $-\frac{181}{284}e^{8} + \frac{292}{71}e^{7} + \frac{205}{71}e^{6} - \frac{3967}{71}e^{5} + \frac{4113}{71}e^{4} + \frac{34399}{284}e^{3} - \frac{14793}{142}e^{2} - \frac{7741}{71}e - \frac{1276}{71}$ |
| 19 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 6w + 3]$ | $-\frac{295}{568}e^{8} + \frac{953}{284}e^{7} + \frac{170}{71}e^{6} - \frac{3262}{71}e^{5} + \frac{6709}{142}e^{4} + \frac{58401}{568}e^{3} - \frac{6435}{71}e^{2} - \frac{12837}{142}e - \frac{788}{71}$ |
| 19 | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 3]$ | $-1$ |
| 25 | $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ | $-\frac{8}{71}e^{8} + \frac{63}{71}e^{7} - \frac{55}{142}e^{6} - \frac{790}{71}e^{5} + \frac{1567}{71}e^{4} + \frac{1003}{71}e^{3} - \frac{2863}{71}e^{2} - \frac{1203}{142}e + \frac{566}{71}$ |
| 29 | $[29, 29, -w^{3} + 4w + 1]$ | $-\frac{217}{568}e^{8} + \frac{779}{284}e^{7} + \frac{36}{71}e^{6} - \frac{2632}{71}e^{5} + \frac{7287}{142}e^{4} + \frac{43847}{568}e^{3} - \frac{7026}{71}e^{2} - \frac{10135}{142}e + \frac{62}{71}$ |
| 41 | $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $-\frac{22}{71}e^{8} + \frac{551}{284}e^{7} + \frac{257}{142}e^{6} - \frac{1924}{71}e^{5} + \frac{1629}{71}e^{4} + \frac{4764}{71}e^{3} - \frac{11897}{284}e^{2} - \frac{4929}{71}e - \frac{893}{71}$ |
| 49 | $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 8w - 4]$ | $-\frac{35}{71}e^{8} + \frac{249}{71}e^{7} + \frac{35}{71}e^{6} - \frac{3261}{71}e^{5} + \frac{4770}{71}e^{4} + \frac{5746}{71}e^{3} - \frac{8239}{71}e^{2} - \frac{5050}{71}e - \frac{346}{71}$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + 2w^{2} - 8w + 2]$ | $-\frac{349}{284}e^{8} + \frac{605}{71}e^{7} + \frac{423}{142}e^{6} - \frac{8221}{71}e^{5} + \frac{10476}{71}e^{4} + \frac{71295}{284}e^{3} - \frac{40417}{142}e^{2} - \frac{35199}{142}e - \frac{1464}{71}$ |
| 59 | $[59, 59, -w^{3} + w^{2} + 2w - 3]$ | $-\frac{171}{142}e^{8} + \frac{2285}{284}e^{7} + \frac{597}{142}e^{6} - \frac{7742}{71}e^{5} + \frac{8995}{71}e^{4} + \frac{33021}{142}e^{3} - \frac{67315}{284}e^{2} - \frac{14791}{71}e - \frac{1539}{71}$ |
| 61 | $[61, 61, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 4w - 2]$ | $-\frac{347}{284}e^{8} + \frac{1211}{142}e^{7} + \frac{211}{71}e^{6} - \frac{8287}{71}e^{5} + \frac{10347}{71}e^{4} + \frac{74541}{284}e^{3} - \frac{19395}{71}e^{2} - \frac{19703}{71}e - \frac{3088}{71}$ |
| 64 | $[64, 2, -2]$ | $-\frac{373}{568}e^{8} + \frac{1127}{284}e^{7} + \frac{679}{142}e^{6} - \frac{4034}{71}e^{5} + \frac{5137}{142}e^{4} + \frac{87723}{568}e^{3} - \frac{4850}{71}e^{2} - \frac{11355}{71}e - \frac{2632}{71}$ |
| 71 | $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 4w + 1]$ | $-\frac{116}{71}e^{8} + \frac{1543}{142}e^{7} + \frac{471}{71}e^{6} - \frac{10674}{71}e^{5} + \frac{11326}{71}e^{4} + \frac{25229}{71}e^{3} - \frac{42415}{142}e^{2} - \frac{25886}{71}e - \frac{4644}{71}$ |
| 71 | $[71, 71, 2w^{4} - 3w^{3} - 5w^{2} + 6w]$ | $-\frac{1}{4}e^{8} + \frac{3}{2}e^{7} + 2e^{6} - 22e^{5} + 11e^{4} + \frac{263}{4}e^{3} - 17e^{2} - 77e - 22$ |
| 79 | $[79, 79, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} + w - 4]$ | $-\frac{52}{71}e^{8} + \frac{677}{142}e^{7} + \frac{265}{71}e^{6} - \frac{4780}{71}e^{5} + \frac{4399}{71}e^{4} + \frac{12235}{71}e^{3} - \frac{17481}{142}e^{2} - \frac{12554}{71}e - \frac{1788}{71}$ |
| 79 | $[79, 79, w^{4} - 3w^{3} - w^{2} + 8w - 3]$ | $\phantom{-}\frac{21}{284}e^{8} - \frac{48}{71}e^{7} + \frac{48}{71}e^{6} + \frac{585}{71}e^{5} - \frac{1390}{71}e^{4} - \frac{1843}{284}e^{3} + \frac{4481}{142}e^{2} - \frac{201}{71}e - \frac{154}{71}$ |
| 89 | $[89, 89, w^{5} - 6w^{3} - w^{2} + 8w]$ | $-\frac{85}{71}e^{8} + \frac{554}{71}e^{7} + \frac{369}{71}e^{6} - \frac{7595}{71}e^{5} + \frac{8085}{71}e^{4} + \frac{17180}{71}e^{3} - \frac{15962}{71}e^{2} - \frac{16007}{71}e - \frac{1530}{71}$ |
| 109 | $[109, 109, -w^{5} + 2w^{4} + 3w^{3} - 6w^{2} - 2w + 5]$ | $\phantom{-}\frac{27}{142}e^{8} - \frac{443}{284}e^{7} + \frac{115}{142}e^{6} + \frac{1413}{71}e^{5} - \frac{2773}{71}e^{4} - \frac{4033}{142}e^{3} + \frac{19769}{284}e^{2} + \frac{1745}{71}e - \frac{609}{71}$ |
| 109 | $[109, 109, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 13w + 11]$ | $-\frac{315}{284}e^{8} + \frac{507}{71}e^{7} + \frac{761}{142}e^{6} - \frac{7000}{71}e^{5} + \frac{6934}{71}e^{4} + \frac{65985}{284}e^{3} - \frac{26461}{142}e^{2} - \frac{33801}{142}e - \frac{2660}{71}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 3]$ | $1$ |