Base field 4.4.19025.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 13 x^2 + 14 x + 44\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, \frac{1}{2} w^3 - 2 w^2 - \frac{5}{2} w + 11]$ |
| 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:
| \(x^8 - x^7 - 19 x^6 + 23 x^5 + 78 x^4 - 105 x^3 - 57 x^2 + 95 x - 23\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^2 - 2 w - 6]$ | $\phantom{-}\frac{217}{1951} e^7 - \frac{116}{1951} e^6 - \frac{4168}{1951} e^5 + \frac{3105}{1951} e^4 + \frac{18551}{1951} e^3 - \frac{14798}{1951} e^2 - \frac{22718}{1951} e + \frac{12172}{1951}$ |
| 4 | $[4, 2, -w^2 + 7]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -\frac{1}{2} w^3 + 2 w^2 + \frac{7}{2} w - 14]$ | $\phantom{-}\frac{505}{3902} e^7 - \frac{225}{3902} e^6 - \frac{4715}{1951} e^5 + \frac{3087}{1951} e^4 + \frac{18992}{1951} e^3 - \frac{28333}{3902} e^2 - \frac{30509}{3902} e + \frac{9551}{1951}$ |
| 5 | $[5, 5, \frac{1}{2} w^3 + \frac{1}{2} w^2 - 6 w - 9]$ | $-\frac{273}{3902} e^7 + \frac{83}{3902} e^6 + \frac{2433}{1951} e^5 - \frac{1607}{1951} e^4 - \frac{8428}{1951} e^3 + \frac{19435}{3902} e^2 + \frac{5861}{3902} e - \frac{8223}{1951}$ |
| 11 | $[11, 11, \frac{1}{2} w^3 - 2 w^2 - \frac{5}{2} w + 11]$ | $\phantom{-}1$ |
| 11 | $[11, 11, \frac{1}{2} w^3 + \frac{1}{2} w^2 - 5 w - 7]$ | $-\frac{856}{1951} e^7 + \frac{53}{1951} e^6 + \frac{15965}{1951} e^5 - \frac{4732}{1951} e^4 - \frac{65509}{1951} e^3 + \frac{26843}{1951} e^2 + \frac{60063}{1951} e - \frac{21573}{1951}$ |
| 31 | $[31, 31, \frac{1}{2} w^2 + \frac{1}{2} w - 4]$ | $-\frac{173}{3902} e^7 + \frac{280}{1951} e^6 + \frac{4177}{3902} e^5 - \frac{5342}{1951} e^4 - \frac{13495}{1951} e^3 + \frac{44461}{3902} e^2 + \frac{19584}{1951} e - \frac{46719}{3902}$ |
| 31 | $[31, 31, -\frac{1}{2} w^2 + \frac{3}{2} w + 3]$ | $\phantom{-}\frac{505}{1951} e^7 - \frac{225}{1951} e^6 - \frac{9430}{1951} e^5 + \frac{6174}{1951} e^4 + \frac{37984}{1951} e^3 - \frac{28333}{1951} e^2 - \frac{34411}{1951} e + \frac{19102}{1951}$ |
| 41 | $[41, 41, \frac{1}{2} w^2 + \frac{1}{2} w - 6]$ | $\phantom{-}\frac{473}{1951} e^7 - \frac{209}{3902} e^6 - \frac{18341}{3902} e^5 + \frac{3882}{1951} e^4 + \frac{41461}{1951} e^3 - \frac{20109}{1951} e^2 - \frac{79447}{3902} e + \frac{30811}{3902}$ |
| 41 | $[41, 41, 2 w^3 - \frac{15}{2} w^2 - \frac{25}{2} w + 50]$ | $-\frac{1107}{3902} e^7 + \frac{179}{1951} e^6 + \frac{21811}{3902} e^5 - \frac{5380}{1951} e^4 - \frac{51584}{1951} e^3 + \frac{50379}{3902} e^2 + \frac{67315}{1951} e - \frac{50415}{3902}$ |
| 41 | $[41, 41, \frac{5}{2} w^2 - \frac{1}{2} w - 17]$ | $-\frac{173}{1951} e^7 + \frac{560}{1951} e^6 + \frac{4177}{1951} e^5 - \frac{10684}{1951} e^4 - \frac{26990}{1951} e^3 + \frac{42510}{1951} e^2 + \frac{45021}{1951} e - \frac{35013}{1951}$ |
| 41 | $[41, 41, \frac{1}{2} w^2 - \frac{3}{2} w - 5]$ | $\phantom{-}\frac{2419}{3902} e^7 - \frac{421}{3902} e^6 - \frac{22566}{1951} e^5 + \frac{9444}{1951} e^4 + \frac{92488}{1951} e^3 - \frac{106619}{3902} e^2 - \frac{171423}{3902} e + \frac{45870}{1951}$ |
| 61 | $[61, 61, -\frac{1}{2} w^3 + w^2 + \frac{7}{2} w - 1]$ | $\phantom{-}\frac{2033}{3902} e^7 + \frac{59}{1951} e^6 - \frac{37673}{3902} e^5 + \frac{4156}{1951} e^4 + \frac{75719}{1951} e^3 - \frac{69849}{3902} e^2 - \frac{61204}{1951} e + \frac{80257}{3902}$ |
| 61 | $[61, 61, -\frac{1}{2} w^3 + \frac{1}{2} w^2 + 4 w - 3]$ | $-\frac{137}{3902} e^7 + \frac{639}{1951} e^6 + \frac{4007}{3902} e^5 - \frac{11369}{1951} e^4 - \frac{15085}{1951} e^3 + \frac{82033}{3902} e^2 + \frac{27023}{1951} e - \frac{57071}{3902}$ |
| 71 | $[71, 71, \frac{1}{2} w^3 + w^2 - \frac{11}{2} w - 13]$ | $-\frac{1477}{1951} e^7 + \frac{349}{1951} e^6 + \frac{27677}{1951} e^5 - \frac{12386}{1951} e^4 - \frac{114057}{1951} e^3 + \frac{57674}{1951} e^2 + \frac{104847}{1951} e - \frac{42003}{1951}$ |
| 71 | $[71, 71, -\frac{1}{2} w^3 + \frac{5}{2} w^2 + 2 w - 17]$ | $\phantom{-}\frac{2141}{3902} e^7 - \frac{815}{1951} e^6 - \frac{42085}{3902} e^5 + \frac{19242}{1951} e^4 + \frac{96312}{1951} e^3 - \frac{167841}{3902} e^2 - \frac{101319}{1951} e + \frac{127241}{3902}$ |
| 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 | $[89, 89, -w^3 + \frac{3}{2} w^2 + \frac{13}{2} w - 9]$ | $\phantom{-}\frac{271}{1951} e^7 - \frac{29}{3902} e^6 - \frac{10797}{3902} e^5 + \frac{632}{1951} e^4 + \frac{25487}{1951} e^3 + \frac{4491}{1951} e^2 - \frac{41773}{3902} e - \frac{39879}{3902}$ |
| 89 | $[89, 89, w^3 - \frac{7}{2} w^2 - \frac{11}{2} w + 20]$ | $\phantom{-}\frac{1095}{3902} e^7 - \frac{949}{1951} e^6 - \frac{23055}{3902} e^5 + \frac{19095}{1951} e^4 + \frac{59918}{1951} e^3 - \frac{152649}{3902} e^2 - \frac{78249}{1951} e + \frac{111095}{3902}$ |
| 89 | $[89, 89, -w^3 - \frac{1}{2} w^2 + \frac{19}{2} w + 12]$ | $-\frac{4317}{3902} e^7 + \frac{1010}{1951} e^6 + \frac{83143}{3902} e^5 - \frac{26934}{1951} e^4 - \frac{182949}{1951} e^3 + \frac{243225}{3902} e^2 + \frac{187981}{1951} e - \frac{206915}{3902}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, \frac{1}{2} w^3 - 2 w^2 - \frac{5}{2} w + 11]$ | $-1$ |