Base field 5.5.170701.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 4x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[16, 4, -2w^{4} + 3w^{3} + 10w^{2} - 4w - 3]$ |
| Dimension: | $9$ |
| 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:
| \(x^{9} + x^{8} - 41x^{7} - 29x^{6} + 548x^{5} + 258x^{4} - 2723x^{3} - 1461x^{2} + 4575x + 3492\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 2]$ | $\phantom{-}e$ |
| 8 | $[8, 2, -2w^{4} + 3w^{3} + 10w^{2} - 5w - 3]$ | $-\frac{632858}{80281923}e^{8} - \frac{2957306}{80281923}e^{7} + \frac{18596809}{80281923}e^{6} + \frac{100656124}{80281923}e^{5} - \frac{116682577}{80281923}e^{4} - \frac{332464287}{26760641}e^{3} - \frac{280234244}{80281923}e^{2} + \frac{972406267}{26760641}e + \frac{810873563}{26760641}$ |
| 11 | $[11, 11, w^{4} - w^{3} - 6w^{2} + 2]$ | $-\frac{235288}{80281923}e^{8} - \frac{523813}{80281923}e^{7} + \frac{8489594}{80281923}e^{6} + \frac{16762280}{80281923}e^{5} - \frac{93124079}{80281923}e^{4} - \frac{46211701}{26760641}e^{3} + \frac{320571728}{80281923}e^{2} + \frac{68424711}{26760641}e - \frac{56046724}{26760641}$ |
| 13 | $[13, 13, -w^{4} + 2w^{3} + 5w^{2} - 5w - 3]$ | $\phantom{-}\frac{1053718}{80281923}e^{8} + \frac{3259606}{80281923}e^{7} - \frac{36757484}{80281923}e^{6} - \frac{102094823}{80281923}e^{5} + \frac{365619773}{80281923}e^{4} + \frac{295881373}{26760641}e^{3} - \frac{865573637}{80281923}e^{2} - \frac{787202230}{26760641}e - \frac{353713766}{26760641}$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}\frac{381169}{26760641}e^{8} + \frac{1092773}{26760641}e^{7} - \frac{12536486}{26760641}e^{6} - \frac{34267642}{26760641}e^{5} + \frac{110307583}{26760641}e^{4} + \frac{296653346}{26760641}e^{3} - \frac{174910584}{26760641}e^{2} - \frac{781999952}{26760641}e - \frac{459582632}{26760641}$ |
| 23 | $[23, 23, -w + 2]$ | $-\frac{370689}{26760641}e^{8} - \frac{741883}{26760641}e^{7} + \frac{12830755}{26760641}e^{6} + \frac{20515128}{26760641}e^{5} - \frac{127953305}{26760641}e^{4} - \frac{137785951}{26760641}e^{3} + \frac{336073331}{26760641}e^{2} + \frac{300033010}{26760641}e + \frac{56011020}{26760641}$ |
| 31 | $[31, 31, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $...$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{589405}{26760641}e^{8} - \frac{1017254}{26760641}e^{7} + \frac{21714178}{26760641}e^{6} + \frac{26582121}{26760641}e^{5} - \frac{241973730}{26760641}e^{4} - \frac{147414738}{26760641}e^{3} + \frac{851627175}{26760641}e^{2} + \frac{210014325}{26760641}e - \frac{751562552}{26760641}$ |
| 47 | $[47, 47, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ | $\phantom{-}\frac{890456}{80281923}e^{8} - \frac{214984}{80281923}e^{7} - \frac{35524870}{80281923}e^{6} + \frac{21580418}{80281923}e^{5} + \frac{445108759}{80281923}e^{4} - \frac{126034731}{26760641}e^{3} - \frac{1887257605}{80281923}e^{2} + \frac{332992918}{26760641}e + \frac{874088928}{26760641}$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $\phantom{-}\frac{483607}{26760641}e^{8} + \frac{283785}{26760641}e^{7} - \frac{17785344}{26760641}e^{6} - \frac{4217415}{26760641}e^{5} + \frac{198886631}{26760641}e^{4} - \frac{32839356}{26760641}e^{3} - \frac{729186392}{26760641}e^{2} + \frac{174585133}{26760641}e + \frac{773270946}{26760641}$ |
| 53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 4w - 3]$ | $-\frac{246273}{26760641}e^{8} - \frac{2500314}{26760641}e^{7} + \frac{5129717}{26760641}e^{6} + \frac{85183933}{26760641}e^{5} + \frac{10326759}{26760641}e^{4} - \frac{833029363}{26760641}e^{3} - \frac{444968610}{26760641}e^{2} + \frac{2192642542}{26760641}e + \frac{1741472818}{26760641}$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 4w - 1]$ | $-\frac{1227840}{26760641}e^{8} - \frac{1684397}{26760641}e^{7} + \frac{45192438}{26760641}e^{6} + \frac{42993465}{26760641}e^{5} - \frac{495106408}{26760641}e^{4} - \frac{243713118}{26760641}e^{3} + \frac{1573875620}{26760641}e^{2} + \frac{609152296}{26760641}e - \frac{859207030}{26760641}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 7w^{2} + 3w + 6]$ | $...$ |
| 71 | $[71, 71, -2w^{4} + 2w^{3} + 11w^{2} - 2]$ | $-\frac{444761}{80281923}e^{8} + \frac{4949236}{80281923}e^{7} + \frac{24253768}{80281923}e^{6} - \frac{184126631}{80281923}e^{5} - \frac{389895040}{80281923}e^{4} + \frac{664610360}{26760641}e^{3} + \frac{1943178199}{80281923}e^{2} - \frac{1844940891}{26760641}e - \frac{1494327028}{26760641}$ |
| 71 | $[71, 71, -w^{4} + 3w^{3} + 3w^{2} - 9w - 1]$ | $\phantom{-}\frac{1386380}{80281923}e^{8} + \frac{1987760}{80281923}e^{7} - \frac{51720811}{80281923}e^{6} - \frac{56258911}{80281923}e^{5} + \frac{554909734}{80281923}e^{4} + \frac{135209759}{26760641}e^{3} - \frac{1382955523}{80281923}e^{2} - \frac{374808795}{26760641}e - \frac{302151716}{26760641}$ |
| 73 | $[73, 73, 2w^{4} - 4w^{3} - 9w^{2} + 10w + 5]$ | $-\frac{2766668}{80281923}e^{8} - \frac{4077968}{80281923}e^{7} + \frac{103541182}{80281923}e^{6} + \frac{115575049}{80281923}e^{5} - \frac{1166591374}{80281923}e^{4} - \frac{280373211}{26760641}e^{3} + \frac{3870156055}{80281923}e^{2} + \frac{758321016}{26760641}e - \frac{598264086}{26760641}$ |
| 79 | $[79, 79, 2w^{4} - 3w^{3} - 11w^{2} + 4w + 8]$ | $\phantom{-}\frac{147414}{26760641}e^{8} + \frac{1105452}{26760641}e^{7} - \frac{2106599}{26760641}e^{6} - \frac{36569309}{26760641}e^{5} - \frac{37524761}{26760641}e^{4} + \frac{345766145}{26760641}e^{3} + \frac{552589652}{26760641}e^{2} - \frac{954652912}{26760641}e - \frac{1528603572}{26760641}$ |
| 83 | $[83, 83, -3w^{4} + 5w^{3} + 15w^{2} - 9w - 10]$ | $-\frac{415333}{80281923}e^{8} - \frac{5402983}{80281923}e^{7} + \frac{3702209}{80281923}e^{6} + \frac{191514908}{80281923}e^{5} + \frac{183751591}{80281923}e^{4} - \frac{662728962}{26760641}e^{3} - \frac{2283903553}{80281923}e^{2} + \frac{1950549715}{26760641}e + \frac{2176356648}{26760641}$ |
| 89 | $[89, 89, w^{3} - w^{2} - 5w + 1]$ | $-\frac{691167}{26760641}e^{8} + \frac{325067}{26760641}e^{7} + \frac{27993202}{26760641}e^{6} - \frac{19206330}{26760641}e^{5} - \frac{350505155}{26760641}e^{4} + \frac{284506733}{26760641}e^{3} + \frac{1402785493}{26760641}e^{2} - \frac{777884175}{26760641}e - \frac{1640824346}{26760641}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $1$ |