Base field 4.4.19025.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 13x^{2} + 14x + 44\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11,11,-\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 5w + 7]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - x^{7} - 19x^{6} + 23x^{5} + 78x^{4} - 105x^{3} - 57x^{2} + 95x - 23\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{2} - 2w - 6]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} + 7]$ | $\phantom{-}\frac{217}{1951}e^{7} - \frac{116}{1951}e^{6} - \frac{4168}{1951}e^{5} + \frac{3105}{1951}e^{4} + \frac{18551}{1951}e^{3} - \frac{14798}{1951}e^{2} - \frac{22718}{1951}e + \frac{12172}{1951}$ |
| 5 | $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ | $-\frac{273}{3902}e^{7} + \frac{83}{3902}e^{6} + \frac{2433}{1951}e^{5} - \frac{1607}{1951}e^{4} - \frac{8428}{1951}e^{3} + \frac{19435}{3902}e^{2} + \frac{5861}{3902}e - \frac{8223}{1951}$ |
| 5 | $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ | $\phantom{-}\frac{505}{3902}e^{7} - \frac{225}{3902}e^{6} - \frac{4715}{1951}e^{5} + \frac{3087}{1951}e^{4} + \frac{18992}{1951}e^{3} - \frac{28333}{3902}e^{2} - \frac{30509}{3902}e + \frac{9551}{1951}$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ | $-\frac{856}{1951}e^{7} + \frac{53}{1951}e^{6} + \frac{15965}{1951}e^{5} - \frac{4732}{1951}e^{4} - \frac{65509}{1951}e^{3} + \frac{26843}{1951}e^{2} + \frac{60063}{1951}e - \frac{21573}{1951}$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ | $\phantom{-}1$ |
| 31 | $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ | $\phantom{-}\frac{505}{1951}e^{7} - \frac{225}{1951}e^{6} - \frac{9430}{1951}e^{5} + \frac{6174}{1951}e^{4} + \frac{37984}{1951}e^{3} - \frac{28333}{1951}e^{2} - \frac{34411}{1951}e + \frac{19102}{1951}$ |
| 31 | $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ | $-\frac{173}{3902}e^{7} + \frac{280}{1951}e^{6} + \frac{4177}{3902}e^{5} - \frac{5342}{1951}e^{4} - \frac{13495}{1951}e^{3} + \frac{44461}{3902}e^{2} + \frac{19584}{1951}e - \frac{46719}{3902}$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ | $\phantom{-}\frac{2419}{3902}e^{7} - \frac{421}{3902}e^{6} - \frac{22566}{1951}e^{5} + \frac{9444}{1951}e^{4} + \frac{92488}{1951}e^{3} - \frac{106619}{3902}e^{2} - \frac{171423}{3902}e + \frac{45870}{1951}$ |
| 41 | $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ | $-\frac{173}{1951}e^{7} + \frac{560}{1951}e^{6} + \frac{4177}{1951}e^{5} - \frac{10684}{1951}e^{4} - \frac{26990}{1951}e^{3} + \frac{42510}{1951}e^{2} + \frac{45021}{1951}e - \frac{35013}{1951}$ |
| 41 | $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ | $-\frac{1107}{3902}e^{7} + \frac{179}{1951}e^{6} + \frac{21811}{3902}e^{5} - \frac{5380}{1951}e^{4} - \frac{51584}{1951}e^{3} + \frac{50379}{3902}e^{2} + \frac{67315}{1951}e - \frac{50415}{3902}$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ | $\phantom{-}\frac{473}{1951}e^{7} - \frac{209}{3902}e^{6} - \frac{18341}{3902}e^{5} + \frac{3882}{1951}e^{4} + \frac{41461}{1951}e^{3} - \frac{20109}{1951}e^{2} - \frac{79447}{3902}e + \frac{30811}{3902}$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ | $-\frac{137}{3902}e^{7} + \frac{639}{1951}e^{6} + \frac{4007}{3902}e^{5} - \frac{11369}{1951}e^{4} - \frac{15085}{1951}e^{3} + \frac{82033}{3902}e^{2} + \frac{27023}{1951}e - \frac{57071}{3902}$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ | $\phantom{-}\frac{2033}{3902}e^{7} + \frac{59}{1951}e^{6} - \frac{37673}{3902}e^{5} + \frac{4156}{1951}e^{4} + \frac{75719}{1951}e^{3} - \frac{69849}{3902}e^{2} - \frac{61204}{1951}e + \frac{80257}{3902}$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ | $\phantom{-}\frac{2141}{3902}e^{7} - \frac{815}{1951}e^{6} - \frac{42085}{3902}e^{5} + \frac{19242}{1951}e^{4} + \frac{96312}{1951}e^{3} - \frac{167841}{3902}e^{2} - \frac{101319}{1951}e + \frac{127241}{3902}$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ | $-\frac{1477}{1951}e^{7} + \frac{349}{1951}e^{6} + \frac{27677}{1951}e^{5} - \frac{12386}{1951}e^{4} - \frac{114057}{1951}e^{3} + \frac{57674}{1951}e^{2} + \frac{104847}{1951}e - \frac{42003}{1951}$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{3669}{3902}e^{7} + \frac{332}{1951}e^{6} - \frac{68377}{3902}e^{5} + \frac{2752}{1951}e^{4} + \frac{141333}{1951}e^{3} - \frac{80591}{3902}e^{2} - \frac{130685}{1951}e + \frac{81091}{3902}$ |
| 89 | $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ | $\phantom{-}\frac{415}{3902}e^{7} - \frac{69}{3902}e^{6} - \frac{3527}{1951}e^{5} + \frac{1571}{1951}e^{4} + \frac{11261}{1951}e^{3} - \frac{13007}{3902}e^{2} - \frac{15027}{3902}e - \frac{4823}{1951}$ |
| 89 | $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ | $-\frac{4317}{3902}e^{7} + \frac{1010}{1951}e^{6} + \frac{83143}{3902}e^{5} - \frac{26934}{1951}e^{4} - \frac{182949}{1951}e^{3} + \frac{243225}{3902}e^{2} + \frac{187981}{1951}e - \frac{206915}{3902}$ |
| 89 | $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ | $\phantom{-}\frac{1095}{3902}e^{7} - \frac{949}{1951}e^{6} - \frac{23055}{3902}e^{5} + \frac{19095}{1951}e^{4} + \frac{59918}{1951}e^{3} - \frac{152649}{3902}e^{2} - \frac{78249}{1951}e + \frac{111095}{3902}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,-\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 5w + 7]$ | $-1$ |