Base field 5.5.180769.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 7x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[32, 2, 2]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 45x^{12} + 698x^{10} - 4465x^{8} + 12090x^{6} - 11284x^{4} + 1080x^{2} - 27\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $\phantom{-}\frac{4428959}{299542521}e^{12} - \frac{66452976}{99847507}e^{10} + \frac{3093687493}{299542521}e^{8} - \frac{19805008715}{299542521}e^{6} + \frac{17886744891}{99847507}e^{4} - \frac{49736070947}{299542521}e^{2} + \frac{1002787341}{99847507}$ |
| 5 | $[5, 5, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ | $\phantom{-}\frac{74379142}{898627563}e^{13} - \frac{371516771}{99847507}e^{11} + \frac{51756410525}{898627563}e^{9} - \frac{329451802525}{898627563}e^{7} + \frac{293555576035}{299542521}e^{5} - \frac{785331522934}{898627563}e^{3} + \frac{3527092194}{99847507}e$ |
| 7 | $[7, 7, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-2$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $-\frac{274071032}{898627563}e^{13} + \frac{1368803285}{99847507}e^{11} - \frac{190665964687}{898627563}e^{9} + \frac{1213697805668}{898627563}e^{7} - \frac{1082581880933}{299542521}e^{5} + \frac{2911121768765}{898627563}e^{3} - \frac{14419421189}{99847507}e$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{10438822}{99847507}e^{12} + \frac{470299886}{99847507}e^{10} - \frac{7306038234}{99847507}e^{8} + \frac{46788765065}{99847507}e^{6} - \frac{126069754872}{99847507}e^{4} + \frac{113784138801}{99847507}e^{2} - \frac{5499737679}{99847507}$ |
| 32 | $[32, 2, 2]$ | $-1$ |
| 37 | $[37, 37, -w^{4} + 2w^{3} + 3w^{2} - 7w + 4]$ | $-\frac{202079017}{898627563}e^{13} + \frac{1009932792}{99847507}e^{11} - \frac{140854679492}{898627563}e^{9} + \frac{898994882503}{898627563}e^{7} - \frac{806474769658}{299542521}e^{5} + \frac{2206041669970}{898627563}e^{3} - \frac{15399412778}{99847507}e$ |
| 41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $-\frac{20035085}{898627563}e^{13} + \frac{99460400}{99847507}e^{11} - \frac{13708610908}{898627563}e^{9} + \frac{85532305757}{898627563}e^{7} - \frac{73652851409}{299542521}e^{5} + \frac{181618679357}{898627563}e^{3} + \frac{534189839}{99847507}e$ |
| 43 | $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 5w - 3]$ | $\phantom{-}\frac{401770907}{898627563}e^{13} - \frac{2007219306}{99847507}e^{11} + \frac{279764233654}{898627563}e^{9} - \frac{1783240885646}{898627563}e^{7} + \frac{1595501074556}{299542521}e^{5} - \frac{4331831915801}{898627563}e^{3} + \frac{26191894266}{99847507}e$ |
| 43 | $[43, 43, -w^{2} + w + 3]$ | $-\frac{5647841}{299542521}e^{12} + \frac{84340576}{99847507}e^{10} - \frac{3896410750}{299542521}e^{8} + \frac{24631891685}{299542521}e^{6} - \frac{21933934797}{99847507}e^{4} + \frac{60656596058}{299542521}e^{2} - \frac{1220749901}{99847507}$ |
| 47 | $[47, 47, 2w^{4} - 3w^{3} - 9w^{2} + 8w + 3]$ | $-\frac{596861768}{898627563}e^{13} + \frac{2980300610}{99847507}e^{11} - \frac{415001145682}{898627563}e^{9} + \frac{2640420302942}{898627563}e^{7} - \frac{2354353128830}{299542521}e^{5} + \frac{6336563713655}{898627563}e^{3} - \frac{33202914777}{99847507}e$ |
| 61 | $[61, 61, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 2]$ | $\phantom{-}\frac{403268155}{898627563}e^{13} - \frac{2014084924}{99847507}e^{11} + \frac{280560391838}{898627563}e^{9} - \frac{1786116467041}{898627563}e^{7} + \frac{1593559510531}{299542521}e^{5} - \frac{4285264761967}{898627563}e^{3} + \frac{20277261279}{99847507}e$ |
| 79 | $[79, 79, w^{2} - w - 5]$ | $\phantom{-}\frac{88798969}{898627563}e^{13} - \frac{442646052}{99847507}e^{11} + \frac{61465977806}{898627563}e^{9} - \frac{389251442503}{898627563}e^{7} + \frac{345015235891}{299542521}e^{5} - \frac{918864580885}{898627563}e^{3} + \frac{3173366345}{99847507}e$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}\frac{753959792}{898627563}e^{13} - \frac{3765455029}{99847507}e^{11} + \frac{524513813059}{898627563}e^{9} - \frac{3339505659494}{898627563}e^{7} + \frac{2981731586375}{299542521}e^{5} - \frac{8050679870549}{898627563}e^{3} + \frac{43489300193}{99847507}e$ |
| 79 | $[79, 79, -2w^{4} + 4w^{3} + 7w^{2} - 14w + 2]$ | $\phantom{-}\frac{935338385}{898627563}e^{13} - \frac{4671069154}{99847507}e^{11} + \frac{650592976744}{898627563}e^{9} - \frac{4141165422521}{898627563}e^{7} + \frac{3695271164573}{299542521}e^{5} - \frac{9967047114515}{898627563}e^{3} + \frac{55067060533}{99847507}e$ |
| 97 | $[97, 97, w^{3} - 6w]$ | $\phantom{-}\frac{157893619}{898627563}e^{13} - \frac{788687244}{99847507}e^{11} + \frac{109885494809}{898627563}e^{9} - \frac{699769764022}{898627563}e^{7} + \frac{624552233566}{299542521}e^{5} - \frac{1683324936523}{898627563}e^{3} + \frac{9924443484}{99847507}e$ |
| 101 | $[101, 101, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $\phantom{-}\frac{20035085}{898627563}e^{13} - \frac{99460400}{99847507}e^{11} + \frac{13708610908}{898627563}e^{9} - \frac{85532305757}{898627563}e^{7} + \frac{73652851409}{299542521}e^{5} - \frac{181618679357}{898627563}e^{3} - \frac{534189839}{99847507}e$ |
| 101 | $[101, 101, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 1]$ | $-\frac{394132820}{898627563}e^{13} + \frac{1968431222}{99847507}e^{11} - \frac{274187718079}{898627563}e^{9} + \frac{1745250308069}{898627563}e^{7} - \frac{1556118429035}{299542521}e^{5} + \frac{4172602871312}{898627563}e^{3} - \frac{17606697197}{99847507}e$ |
| 107 | $[107, 107, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 2]$ | $\phantom{-}\frac{69300344}{299542521}e^{12} - \frac{1038685030}{99847507}e^{10} + \frac{48258944974}{299542521}e^{8} - \frac{307616834648}{299542521}e^{6} + \frac{275158345902}{99847507}e^{4} - \frac{744855537020}{299542521}e^{2} + \frac{11551997034}{99847507}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $32$ | $[32,2,2]$ | $1$ |