Base field 6.6.1541581.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 2x^{3} + 9x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + 6x^{8} - 7x^{7} - 84x^{6} - 21x^{5} + 398x^{4} + 215x^{3} - 743x^{2} - 348x + 430\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ | $\phantom{-}\frac{1397}{6337}e^{8} + \frac{6247}{6337}e^{7} - \frac{18682}{6337}e^{6} - \frac{84873}{6337}e^{5} + \frac{97891}{6337}e^{4} + \frac{362401}{6337}e^{3} - \frac{279363}{6337}e^{2} - \frac{486415}{6337}e + \frac{329145}{6337}$ |
| 11 | $[11, 11, w^{2} - w - 2]$ | $-\frac{4808}{19011}e^{8} - \frac{21305}{19011}e^{7} + \frac{20445}{6337}e^{6} + \frac{92283}{6337}e^{5} - \frac{99875}{6337}e^{4} - \frac{1117600}{19011}e^{3} + \frac{813694}{19011}e^{2} + \frac{1409441}{19011}e - \frac{1016680}{19011}$ |
| 17 | $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ | $-\frac{4466}{19011}e^{8} - \frac{18374}{19011}e^{7} + \frac{22436}{6337}e^{6} + \frac{86101}{6337}e^{5} - \frac{130943}{6337}e^{4} - \frac{1155997}{19011}e^{3} + \frac{1083541}{19011}e^{2} + \frac{1641269}{19011}e - \frac{1130866}{19011}$ |
| 27 | $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}1$ |
| 27 | $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{1100}{6337}e^{8} + \frac{4869}{6337}e^{7} - \frac{13363}{6337}e^{6} - \frac{59095}{6337}e^{5} + \frac{67100}{6337}e^{4} + \frac{218143}{6337}e^{3} - \frac{202357}{6337}e^{2} - \frac{252821}{6337}e + \frac{250537}{6337}$ |
| 37 | $[37, 37, -w^{2} + 2w + 2]$ | $-\frac{7297}{19011}e^{8} - \frac{28906}{19011}e^{7} + \frac{37992}{6337}e^{6} + \frac{135866}{6337}e^{5} - \frac{228641}{6337}e^{4} - \frac{1819334}{19011}e^{3} + \frac{1932758}{19011}e^{2} + \frac{2521090}{19011}e - \frac{2050850}{19011}$ |
| 47 | $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ | $\phantom{-}\frac{8864}{19011}e^{8} + \frac{35387}{19011}e^{7} - \frac{50419}{6337}e^{6} - \frac{184388}{6337}e^{5} + \frac{321761}{6337}e^{4} + \frac{2733757}{19011}e^{3} - \frac{2768386}{19011}e^{2} - \frac{4112864}{19011}e + \frac{2905684}{19011}$ |
| 53 | $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ | $-\frac{5334}{6337}e^{8} - \frac{22700}{6337}e^{7} + \frac{82277}{6337}e^{6} + \frac{333278}{6337}e^{5} - \frac{502810}{6337}e^{4} - \frac{1561725}{6337}e^{3} + \frac{1505640}{6337}e^{2} + \frac{2269702}{6337}e - \frac{1691108}{6337}$ |
| 59 | $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{2125}{6337}e^{8} + \frac{9262}{6337}e^{7} - \frac{26535}{6337}e^{6} - \frac{115457}{6337}e^{5} + \frac{129625}{6337}e^{4} + \frac{442872}{6337}e^{3} - \frac{359664}{6337}e^{2} - \frac{537804}{6337}e + \frac{402043}{6337}$ |
| 64 | $[64, 2, -2]$ | $-\frac{202}{6337}e^{8} - \frac{1620}{6337}e^{7} - \frac{415}{6337}e^{6} + \frac{18514}{6337}e^{5} + \frac{13026}{6337}e^{4} - \frac{73599}{6337}e^{3} - \frac{9630}{6337}e^{2} + \frac{109993}{6337}e - \frac{63855}{6337}$ |
| 67 | $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ | $\phantom{-}\frac{6613}{19011}e^{8} + \frac{23044}{19011}e^{7} - \frac{41974}{6337}e^{6} - \frac{123502}{6337}e^{5} + \frac{290777}{6337}e^{4} + \frac{1896128}{19011}e^{3} - \frac{2529485}{19011}e^{2} - \frac{3041779}{19011}e + \frac{2469332}{19011}$ |
| 67 | $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ | $-\frac{790}{19011}e^{8} + \frac{9350}{19011}e^{7} + \frac{29680}{6337}e^{6} + \frac{1569}{6337}e^{5} - \frac{299116}{6337}e^{4} - \frac{684308}{19011}e^{3} + \frac{2624882}{19011}e^{2} + \frac{1833973}{19011}e - \frac{2013110}{19011}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $-\frac{1567}{6337}e^{8} - \frac{6481}{6337}e^{7} + \frac{24607}{6337}e^{6} + \frac{94870}{6337}e^{5} - \frac{152620}{6337}e^{4} - \frac{445485}{6337}e^{3} + \frac{461745}{6337}e^{2} + \frac{641224}{6337}e - \frac{550658}{6337}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $-\frac{4513}{19011}e^{8} - \frac{22390}{19011}e^{7} + \frac{12731}{6337}e^{6} + \frac{85320}{6337}e^{5} - \frac{13608}{6337}e^{4} - \frac{819473}{19011}e^{3} - \frac{126055}{19011}e^{2} + \frac{678760}{19011}e - \frac{64010}{19011}$ |
| 73 | $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ | $\phantom{-}\frac{7586}{19011}e^{8} + \frac{39443}{19011}e^{7} - \frac{25507}{6337}e^{6} - \frac{169625}{6337}e^{5} + \frac{92991}{6337}e^{4} + \frac{2027749}{19011}e^{3} - \frac{898096}{19011}e^{2} - \frac{2423690}{19011}e + \frac{1595374}{19011}$ |
| 83 | $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ | $-\frac{19618}{19011}e^{8} - \frac{97978}{19011}e^{7} + \frac{69490}{6337}e^{6} + \frac{419616}{6337}e^{5} - \frac{270047}{6337}e^{4} - \frac{5058206}{19011}e^{3} + \frac{2318513}{19011}e^{2} + \frac{6339223}{19011}e - \frac{3607430}{19011}$ |
| 83 | $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ | $\phantom{-}\frac{217}{6337}e^{8} - \frac{2087}{6337}e^{7} - \frac{21169}{6337}e^{6} - \frac{1317}{6337}e^{5} + \frac{216021}{6337}e^{4} + \frac{164802}{6337}e^{3} - \frac{658428}{6337}e^{2} - \frac{447026}{6337}e + \frac{517112}{6337}$ |
| 89 | $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ | $-\frac{4531}{6337}e^{8} - \frac{19209}{6337}e^{7} + \frac{67896}{6337}e^{6} + \frac{274613}{6337}e^{5} - \frac{396794}{6337}e^{4} - \frac{1240697}{6337}e^{3} + \frac{1133146}{6337}e^{2} + \frac{1737178}{6337}e - \frac{1215003}{6337}$ |
| 97 | $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ | $\phantom{-}\frac{22943}{19011}e^{8} + \frac{102182}{19011}e^{7} - \frac{100477}{6337}e^{6} - \frac{455779}{6337}e^{5} + \frac{512979}{6337}e^{4} + \frac{5775922}{19011}e^{3} - \frac{4235461}{19011}e^{2} - \frac{7674194}{19011}e + \frac{5023639}{19011}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ | $-1$ |