Base field 4.4.18736.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, w^{2} - 2w - 4]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 35x^{14} + 486x^{12} - 3437x^{10} + 13176x^{8} - 26864x^{6} + 26528x^{4} - 10608x^{2} + 1152\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}\frac{49}{36416}e^{15} - \frac{6055}{109248}e^{13} + \frac{512}{569}e^{11} - \frac{266133}{36416}e^{9} + \frac{1696255}{54624}e^{7} - \frac{1778285}{27312}e^{5} + \frac{750473}{13656}e^{3} - \frac{6064}{569}e$ |
| 5 | $[5, 5, w]$ | $-\frac{509}{327744}e^{15} + \frac{17281}{327744}e^{13} - \frac{9743}{13656}e^{11} + \frac{1627825}{327744}e^{9} - \frac{1033655}{54624}e^{7} + \frac{3101275}{81936}e^{5} - \frac{1346165}{40968}e^{3} + \frac{25021}{3414}e$ |
| 7 | $[7, 7, w - 2]$ | $-\frac{53}{54624}e^{14} + \frac{529}{18208}e^{12} - \frac{2977}{9104}e^{10} + \frac{96349}{54624}e^{8} - \frac{69337}{13656}e^{6} + \frac{133943}{13656}e^{4} - \frac{16051}{1138}e^{2} + \frac{2716}{569}$ |
| 11 | $[11, 11, w^{2} - 2w - 4]$ | $-1$ |
| 23 | $[23, 23, -w^{2} + 2w + 1]$ | $-\frac{13}{3414}e^{15} + \frac{200}{1707}e^{13} - \frac{6153}{4552}e^{11} + \frac{100103}{13656}e^{9} - \frac{33542}{1707}e^{7} + \frac{132317}{4552}e^{5} - \frac{229919}{6828}e^{3} + \frac{10863}{569}e$ |
| 23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}\frac{1897}{163872}e^{15} - \frac{64103}{163872}e^{13} + \frac{141553}{27312}e^{11} - \frac{5635073}{163872}e^{9} + \frac{1644281}{13656}e^{7} - \frac{8759327}{40968}e^{5} + \frac{847999}{5121}e^{3} - \frac{61784}{1707}e$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 6w + 2]$ | $\phantom{-}\frac{2725}{327744}e^{15} - \frac{90893}{327744}e^{13} + \frac{98717}{27312}e^{11} - \frac{7688729}{327744}e^{9} + \frac{1446063}{18208}e^{7} - \frac{10854125}{81936}e^{5} + \frac{3701167}{40968}e^{3} - \frac{35263}{1707}e$ |
| 31 | $[31, 31, -w^{3} + 3w^{2} + w - 1]$ | $-\frac{49}{18208}e^{14} + \frac{6055}{54624}e^{12} - \frac{1024}{569}e^{10} + \frac{266133}{18208}e^{8} - \frac{1696255}{27312}e^{6} + \frac{1778285}{13656}e^{4} - \frac{750473}{6828}e^{2} + \frac{13266}{569}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{155}{163872}e^{15} + \frac{4813}{163872}e^{13} - \frac{9329}{27312}e^{11} + \frac{304063}{163872}e^{9} - \frac{22111}{4552}e^{7} + \frac{32876}{5121}e^{5} - \frac{147269}{20484}e^{3} + \frac{17251}{1707}e$ |
| 37 | $[37, 37, w^{2} - 2w - 6]$ | $-\frac{7}{6828}e^{14} + \frac{129}{4552}e^{12} - \frac{1197}{4552}e^{10} + \frac{1112}{1707}e^{8} + \frac{55343}{13656}e^{6} - \frac{47111}{1707}e^{4} + \frac{56785}{1138}e^{2} - \frac{10228}{569}$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{1733}{163872}e^{15} - \frac{55993}{163872}e^{13} + \frac{28799}{6828}e^{11} - \frac{4079425}{163872}e^{9} + \frac{642521}{9104}e^{7} - \frac{3216175}{40968}e^{5} - \frac{13708}{5121}e^{3} + \frac{101269}{3414}e$ |
| 43 | $[43, 43, w^{2} - 3w - 2]$ | $\phantom{-}\frac{155}{81936}e^{15} - \frac{4813}{81936}e^{13} + \frac{9329}{13656}e^{11} - \frac{304063}{81936}e^{9} + \frac{22111}{2276}e^{7} - \frac{65752}{5121}e^{5} + \frac{126785}{10242}e^{3} - \frac{8897}{1707}e$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 2w - 2]$ | $\phantom{-}\frac{295}{81936}e^{15} - \frac{9821}{81936}e^{13} + \frac{5251}{3414}e^{11} - \frac{792461}{81936}e^{9} + \frac{72331}{2276}e^{7} - \frac{2307643}{40968}e^{5} + \frac{290717}{5121}e^{3} - \frac{97025}{3414}e$ |
| 73 | $[73, 73, w^{3} - 3w^{2} - 2w + 3]$ | $\phantom{-}\frac{26}{1707}e^{15} - \frac{2323}{4552}e^{13} + \frac{15151}{2276}e^{11} - \frac{586475}{13656}e^{9} + \frac{1953587}{13656}e^{7} - \frac{3178159}{13656}e^{5} + \frac{89537}{569}e^{3} - \frac{41953}{1138}e$ |
| 83 | $[83, 83, -w - 3]$ | $\phantom{-}\frac{437}{27312}e^{14} - \frac{1637}{3414}e^{12} + \frac{48459}{9104}e^{10} - \frac{733939}{27312}e^{8} + \frac{538339}{9104}e^{6} - \frac{133109}{3414}e^{4} - \frac{97463}{6828}e^{2} + \frac{11446}{569}$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}\frac{403}{163872}e^{15} - \frac{18659}{163872}e^{13} + \frac{3415}{1707}e^{11} - \frac{2793899}{163872}e^{9} + \frac{673849}{9104}e^{7} - \frac{789103}{5121}e^{5} + \frac{2541913}{20484}e^{3} - \frac{81853}{3414}e$ |
| 89 | $[89, 89, 2w - 1]$ | $-\frac{2585}{327744}e^{15} + \frac{85885}{327744}e^{13} - \frac{46013}{13656}e^{11} + \frac{6964765}{327744}e^{9} - \frac{1251169}{18208}e^{7} + \frac{9018487}{81936}e^{5} - \frac{3364301}{40968}e^{3} + \frac{88699}{3414}e$ |
| 101 | $[101, 101, w^{3} - 4w^{2} + w + 7]$ | $-\frac{41}{18208}e^{14} + \frac{4091}{54624}e^{12} - \frac{4265}{4552}e^{10} + \frac{100429}{18208}e^{8} - \frac{448973}{27312}e^{6} + \frac{421879}{13656}e^{4} - \frac{329605}{6828}e^{2} + \frac{12122}{569}$ |
| 101 | $[101, 101, 2w^{2} - 3w - 3]$ | $\phantom{-}\frac{5411}{163872}e^{15} - \frac{182293}{163872}e^{13} + \frac{401309}{27312}e^{11} - \frac{15928423}{163872}e^{9} + \frac{1543841}{4552}e^{7} - \frac{12248177}{20484}e^{5} + \frac{4643587}{10242}e^{3} - \frac{332441}{3414}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w^{2} - 2w - 4]$ | $1$ |