Base field 6.6.1995125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 6x^{3} + 12x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[11, 11, w - 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 12x^{7} + 26x^{6} + 162x^{5} - 719x^{4} + 606x^{3} + 280x^{2} - 170x - 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w + 2]$ | $\phantom{-}\frac{796}{21785}e^{7} - \frac{22089}{43570}e^{6} + \frac{63747}{43570}e^{5} + \frac{141352}{21785}e^{4} - \frac{1522223}{43570}e^{3} + \frac{677246}{21785}e^{2} + \frac{101879}{8714}e - \frac{37649}{8714}$ |
| 11 | $[11, 11, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 1]$ | $-1$ |
| 19 | $[19, 19, w^{3} - w^{2} - 4w]$ | $-\frac{5883}{43570}e^{7} + \frac{23113}{21785}e^{6} + \frac{38127}{43570}e^{5} - \frac{803961}{43570}e^{4} + \frac{990897}{43570}e^{3} + \frac{586907}{43570}e^{2} - \frac{57736}{4357}e - \frac{32239}{8714}$ |
| 19 | $[19, 19, -w^{5} + 2w^{4} + 6w^{3} - 7w^{2} - 10w + 1]$ | $-\frac{7829}{43570}e^{7} + \frac{28444}{21785}e^{6} + \frac{81911}{43570}e^{5} - \frac{1005243}{43570}e^{4} + \frac{768701}{43570}e^{3} + \frac{924391}{43570}e^{2} - \frac{34989}{4357}e + \frac{19425}{8714}$ |
| 29 | $[29, 29, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 3w - 3]$ | $\phantom{-}\frac{6036}{21785}e^{7} - \frac{51072}{21785}e^{6} - \frac{8724}{21785}e^{5} + \frac{830802}{21785}e^{4} - \frac{1502514}{21785}e^{3} + \frac{293536}{21785}e^{2} + \frac{71088}{4357}e - \frac{7382}{4357}$ |
| 29 | $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$ | $-\frac{5859}{43570}e^{7} + \frac{45893}{43570}e^{6} + \frac{15603}{21785}e^{5} - \frac{740803}{43570}e^{4} + \frac{517473}{21785}e^{3} - \frac{377049}{43570}e^{2} + \frac{79611}{8714}e + \frac{3455}{4357}$ |
| 29 | $[29, 29, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 2w + 1]$ | $\phantom{-}\frac{1206}{21785}e^{7} - \frac{11287}{21785}e^{6} + \frac{6226}{21785}e^{5} + \frac{178252}{21785}e^{4} - \frac{449754}{21785}e^{3} + \frac{141761}{21785}e^{2} + \frac{70472}{4357}e + \frac{1141}{4357}$ |
| 29 | $[29, 29, -w^{4} + 4w^{3} - 9w]$ | $\phantom{-}\frac{3525}{8714}e^{7} - \frac{27669}{8714}e^{6} - \frac{10746}{4357}e^{5} + \frac{469745}{8714}e^{4} - \frac{301674}{4357}e^{3} - \frac{159353}{8714}e^{2} + \frac{186189}{8714}e + \frac{20070}{4357}$ |
| 31 | $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ | $\phantom{-}\frac{3427}{43570}e^{7} - \frac{16967}{21785}e^{6} + \frac{38357}{43570}e^{5} + \frac{469639}{43570}e^{4} - \frac{1555493}{43570}e^{3} + \frac{1564897}{43570}e^{2} - \frac{12562}{4357}e - \frac{97731}{8714}$ |
| 41 | $[41, 41, -2w^{5} + 6w^{4} + 5w^{3} - 15w^{2} - 6w + 3]$ | $-\frac{4247}{43570}e^{7} + \frac{34419}{43570}e^{6} + \frac{6469}{21785}e^{5} - \frac{543439}{43570}e^{4} + \frac{466389}{21785}e^{3} - \frac{493927}{43570}e^{2} - \frac{13941}{8714}e + \frac{24543}{4357}$ |
| 59 | $[59, 59, -2w^{5} + 6w^{4} + 6w^{3} - 16w^{2} - 11w + 1]$ | $-\frac{8646}{21785}e^{7} + \frac{70947}{21785}e^{6} + \frac{26139}{21785}e^{5} - \frac{1152842}{21785}e^{4} + \frac{1913354}{21785}e^{3} - \frac{445236}{21785}e^{2} - \frac{71042}{4357}e + \frac{44841}{4357}$ |
| 61 | $[61, 61, -2w^{5} + 6w^{4} + 5w^{3} - 14w^{2} - 7w]$ | $\phantom{-}\frac{1528}{4357}e^{7} - \frac{12487}{4357}e^{6} - \frac{4937}{4357}e^{5} + \frac{202875}{4357}e^{4} - \frac{332587}{4357}e^{3} + \frac{80715}{4357}e^{2} + \frac{54837}{4357}e - \frac{40706}{4357}$ |
| 61 | $[61, 61, 2w^{5} - 5w^{4} - 8w^{3} + 13w^{2} + 13w + 1]$ | $\phantom{-}\frac{17183}{43570}e^{7} - \frac{63383}{21785}e^{6} - \frac{170617}{43570}e^{5} + \frac{2256661}{43570}e^{4} - \frac{1850987}{43570}e^{3} - \frac{2425297}{43570}e^{2} + \frac{97417}{4357}e + \frac{112483}{8714}$ |
| 61 | $[61, 61, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w - 1]$ | $-\frac{1859}{43570}e^{7} + \frac{6089}{21785}e^{6} + \frac{32311}{43570}e^{5} - \frac{250093}{43570}e^{4} - \frac{10779}{43570}e^{3} + \frac{753551}{43570}e^{2} - \frac{34040}{4357}e + \frac{12219}{8714}$ |
| 61 | $[61, 61, w^{3} - 2w^{2} - 3w - 1]$ | $-\frac{2412}{21785}e^{7} + \frac{22574}{21785}e^{6} - \frac{12452}{21785}e^{5} - \frac{356504}{21785}e^{4} + \frac{899508}{21785}e^{3} - \frac{305307}{21785}e^{2} - \frac{132230}{4357}e + \frac{28217}{4357}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{10613}{43570}e^{7} - \frac{47758}{21785}e^{6} + \frac{30223}{43570}e^{5} + \frac{1491081}{43570}e^{4} - \frac{3414477}{43570}e^{3} + \frac{1540823}{43570}e^{2} + \frac{95672}{4357}e - \frac{35563}{8714}$ |
| 79 | $[79, 79, -3w^{5} + 9w^{4} + 7w^{3} - 21w^{2} - 9w + 2]$ | $\phantom{-}\frac{5067}{43570}e^{7} - \frac{17452}{21785}e^{6} - \frac{64233}{43570}e^{5} + \frac{617239}{43570}e^{4} - \frac{310063}{43570}e^{3} - \frac{577043}{43570}e^{2} + \frac{30860}{4357}e - \frac{17869}{8714}$ |
| 89 | $[89, 89, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 3w + 3]$ | $-\frac{7343}{43570}e^{7} + \frac{55591}{43570}e^{6} + \frac{28066}{21785}e^{5} - \frac{935361}{43570}e^{4} + \frac{533526}{21785}e^{3} + \frac{117597}{43570}e^{2} - \frac{78971}{8714}e + \frac{28671}{4357}$ |
| 101 | $[101, 101, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 5w]$ | $\phantom{-}\frac{728}{21785}e^{7} - \frac{10101}{21785}e^{6} + \frac{29698}{21785}e^{5} + \frac{122161}{21785}e^{4} - \frac{689852}{21785}e^{3} + \frac{743423}{21785}e^{2} + \frac{6521}{4357}e - \frac{22274}{4357}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w - 1]$ | $1$ |