Base field 3.3.1573.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, -w^{2} + 5]$ |
| Dimension: | $17$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{17} - 4x^{16} - 22x^{15} + 103x^{14} + 160x^{13} - 1019x^{12} - 309x^{11} + 4873x^{10} - 1166x^{9} - 11821x^{8} + 5385x^{7} + 14542x^{6} - 7055x^{5} - 8208x^{4} + 3394x^{3} + 1198x^{2} - 660x + 72\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w^{2} - w - 7]$ | $-\frac{255787}{3801738}e^{16} + \frac{851443}{3801738}e^{15} + \frac{12329099}{7603476}e^{14} - \frac{11061875}{1900869}e^{13} - \frac{109337693}{7603476}e^{12} + \frac{443098219}{7603476}e^{11} + \frac{142161577}{2534492}e^{10} - \frac{1076437291}{3801738}e^{9} - \frac{326206267}{3801738}e^{8} + \frac{5314232687}{7603476}e^{7} + \frac{7715311}{633623}e^{6} - \frac{1644347474}{1900869}e^{5} + \frac{572846233}{7603476}e^{4} + \frac{306183885}{633623}e^{3} - \frac{233685283}{3801738}e^{2} - \frac{335675329}{3801738}e + \frac{11170155}{633623}$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}\frac{115045}{2534492}e^{16} - \frac{673225}{2534492}e^{15} - \frac{2320211}{2534492}e^{14} + \frac{8898959}{1267246}e^{13} + \frac{6480339}{1267246}e^{12} - \frac{183327895}{2534492}e^{11} + \frac{8884801}{1267246}e^{10} + \frac{934648765}{2534492}e^{9} - \frac{377128665}{2534492}e^{8} - \frac{1253925607}{1267246}e^{7} + \frac{1121614119}{2534492}e^{6} + \frac{3543066637}{2534492}e^{5} - \frac{580716073}{1267246}e^{4} - \frac{1162659353}{1267246}e^{3} + \frac{159036545}{1267246}e^{2} + \frac{92293610}{633623}e - \frac{18727053}{633623}$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{759487}{3801738}e^{16} - \frac{3125875}{3801738}e^{15} - \frac{16692673}{3801738}e^{14} + \frac{80699161}{3801738}e^{13} + \frac{121910911}{3801738}e^{12} - \frac{802070303}{3801738}e^{11} - \frac{83664279}{1267246}e^{10} + \frac{3869966761}{3801738}e^{9} - \frac{708890021}{3801738}e^{8} - \frac{4780012904}{1900869}e^{7} + \frac{541493353}{633623}e^{6} + \frac{6090560366}{1900869}e^{5} - \frac{3518924783}{3801738}e^{4} - \frac{1210891782}{633623}e^{3} + \frac{470670923}{1900869}e^{2} + \frac{558178952}{1900869}e - \frac{35477972}{633623}$ |
| 11 | $[11, 11, -w^{2} + 5]$ | $\phantom{-}1$ |
| 13 | $[13, 13, w + 3]$ | $-\frac{565739}{1900869}e^{16} + \frac{6534767}{7603476}e^{15} + \frac{14013917}{1900869}e^{14} - \frac{170271683}{7603476}e^{13} - \frac{522032027}{7603476}e^{12} + \frac{1711757515}{7603476}e^{11} + \frac{187911959}{633623}e^{10} - \frac{4182604681}{3801738}e^{9} - \frac{4557840155}{7603476}e^{8} + \frac{10417857019}{3801738}e^{7} + \frac{685254917}{1267246}e^{6} - \frac{26108131343}{7603476}e^{5} - \frac{725960161}{3801738}e^{4} + \frac{1219984928}{633623}e^{3} - \frac{39507469}{3801738}e^{2} - \frac{589124459}{1900869}e + \frac{31331160}{633623}$ |
| 13 | $[13, 13, -2w + 1]$ | $\phantom{-}\frac{164093}{1900869}e^{16} - \frac{1270445}{7603476}e^{15} - \frac{8462497}{3801738}e^{14} + \frac{33016253}{7603476}e^{13} + \frac{168207197}{7603476}e^{12} - \frac{329714845}{7603476}e^{11} - \frac{135447473}{1267246}e^{10} + \frac{396893870}{1900869}e^{9} + \frac{2009900621}{7603476}e^{8} - \frac{957898568}{1900869}e^{7} - \frac{423379749}{1267246}e^{6} + \frac{4511340587}{7603476}e^{5} + \frac{726487993}{3801738}e^{4} - \frac{377229553}{1267246}e^{3} - \frac{73461233}{3801738}e^{2} + \frac{82526648}{1900869}e - \frac{4679246}{633623}$ |
| 19 | $[19, 19, 2w^{2} - w - 15]$ | $\phantom{-}\frac{1263305}{3801738}e^{16} - \frac{4982309}{3801738}e^{15} - \frac{28739705}{3801738}e^{14} + \frac{64781134}{1900869}e^{13} + \frac{226633739}{3801738}e^{12} - \frac{650538260}{1900869}e^{11} - \frac{105919951}{633623}e^{10} + \frac{3185526067}{1900869}e^{9} - \frac{271806175}{3801738}e^{8} - \frac{8024839255}{1900869}e^{7} + \frac{1244924349}{1267246}e^{6} + \frac{10410084445}{1900869}e^{5} - \frac{4747457857}{3801738}e^{4} - \frac{4172863605}{1267246}e^{3} + \frac{778201408}{1900869}e^{2} + \frac{1008030067}{1900869}e - \frac{64824966}{633623}$ |
| 25 | $[25, 5, w^{2} - 7]$ | $\phantom{-}\frac{2627987}{7603476}e^{16} - \frac{2416097}{1900869}e^{15} - \frac{61245899}{7603476}e^{14} + \frac{253295417}{7603476}e^{13} + \frac{507099281}{7603476}e^{12} - \frac{1286224073}{3801738}e^{11} - \frac{274216291}{1267246}e^{10} + \frac{12809904155}{7603476}e^{9} + \frac{380934631}{3801738}e^{8} - \frac{16540895893}{3801738}e^{7} + \frac{1782770407}{2534492}e^{6} + \frac{11077474097}{1900869}e^{5} - \frac{4040229275}{3801738}e^{4} - \frac{2299438215}{633623}e^{3} + \frac{702585170}{1900869}e^{2} + \frac{1157264915}{1900869}e - \frac{73341305}{633623}$ |
| 27 | $[27, 3, 3]$ | $-\frac{153154}{633623}e^{16} + \frac{2524909}{2534492}e^{15} + \frac{3397583}{633623}e^{14} - \frac{65690745}{2534492}e^{13} - \frac{100973557}{2534492}e^{12} + \frac{660425325}{2534492}e^{11} + \frac{55087297}{633623}e^{10} - \frac{1621493309}{1267246}e^{9} + \frac{541081755}{2534492}e^{8} + \frac{4113327181}{1267246}e^{7} - \frac{1358713879}{1267246}e^{6} - \frac{10841585137}{2534492}e^{5} + \frac{1561625923}{1267246}e^{4} + \frac{1671344225}{633623}e^{3} - \frac{445601491}{1267246}e^{2} - \frac{262759003}{633623}e + \frac{50355965}{633623}$ |
| 31 | $[31, 31, w^{2} - 2w - 1]$ | $\phantom{-}\frac{80273}{3801738}e^{16} + \frac{1575533}{7603476}e^{15} - \frac{4098923}{3801738}e^{14} - \frac{39887069}{7603476}e^{13} + \frac{143060761}{7603476}e^{12} + \frac{388229323}{7603476}e^{11} - \frac{193944771}{1267246}e^{10} - \frac{923304439}{3801738}e^{9} + \frac{4732505731}{7603476}e^{8} + \frac{2329995985}{3801738}e^{7} - \frac{1537227699}{1267246}e^{6} - \frac{6703724561}{7603476}e^{5} + \frac{3676368281}{3801738}e^{4} + \frac{831223685}{1267246}e^{3} - \frac{574044679}{3801738}e^{2} - \frac{166589141}{1900869}e + \frac{10359285}{633623}$ |
| 37 | $[37, 37, -3w^{2} + 2w + 23]$ | $\phantom{-}\frac{2971831}{7603476}e^{16} - \frac{9330349}{7603476}e^{15} - \frac{72296839}{7603476}e^{14} + \frac{121563329}{3801738}e^{13} + \frac{162958285}{1900869}e^{12} - \frac{2445826541}{7603476}e^{11} - \frac{438645589}{1267246}e^{10} + \frac{11979392575}{7603476}e^{9} + \frac{4450823515}{7603476}e^{8} - \frac{7506515662}{1900869}e^{7} - \frac{625775055}{2534492}e^{6} + \frac{38238749491}{7603476}e^{5} - \frac{981506779}{3801738}e^{4} - \frac{3712284801}{1267246}e^{3} + \frac{940741751}{3801738}e^{2} + \frac{982605781}{1900869}e - \frac{62389380}{633623}$ |
| 41 | $[41, 41, -2w - 1]$ | $-\frac{325233}{2534492}e^{16} + \frac{246170}{633623}e^{15} + \frac{7649671}{2534492}e^{14} - \frac{24719413}{2534492}e^{13} - \frac{64957451}{2534492}e^{12} + \frac{58639054}{633623}e^{11} + \frac{115046855}{1267246}e^{10} - \frac{1040979741}{2534492}e^{9} - \frac{121886455}{1267246}e^{8} + \frac{545879267}{633623}e^{7} - \frac{286456353}{2534492}e^{6} - \frac{1006892167}{1267246}e^{5} + \frac{374417087}{1267246}e^{4} + \frac{163213507}{633623}e^{3} - \frac{133007176}{633623}e^{2} - \frac{24990350}{633623}e + \frac{14734428}{633623}$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{182411}{633623}e^{16} + \frac{2187691}{2534492}e^{15} + \frac{8919421}{1267246}e^{14} - \frac{56898873}{2534492}e^{13} - \frac{162374679}{2534492}e^{12} + \frac{570497921}{2534492}e^{11} + \frac{167480252}{633623}e^{10} - \frac{1388781717}{1267246}e^{9} - \frac{1208648379}{2534492}e^{8} + \frac{1721579085}{633623}e^{7} + \frac{184513192}{633623}e^{6} - \frac{8605365649}{2534492}e^{5} + \frac{91491815}{1267246}e^{4} + \frac{1214161193}{633623}e^{3} - \frac{171261021}{1267246}e^{2} - \frac{206096760}{633623}e + \frac{38435925}{633623}$ |
| 49 | $[49, 7, w^{2} - 2w - 5]$ | $-\frac{659671}{1900869}e^{16} + \frac{11528965}{7603476}e^{15} + \frac{29455409}{3801738}e^{14} - \frac{300989929}{7603476}e^{13} - \frac{445284475}{7603476}e^{12} + \frac{3041559839}{7603476}e^{11} + \frac{177258769}{1267246}e^{10} - \frac{7523786081}{3801738}e^{9} + \frac{1697451743}{7603476}e^{8} + \frac{9636579019}{1900869}e^{7} - \frac{1654509131}{1267246}e^{6} - \frac{51197874193}{7603476}e^{5} + \frac{2820207929}{1900869}e^{4} + \frac{2630015667}{633623}e^{3} - \frac{1604456597}{3801738}e^{2} - \frac{1272490294}{1900869}e + \frac{80498533}{633623}$ |
| 59 | $[59, 59, 2w - 3]$ | $\phantom{-}\frac{34177}{1267246}e^{16} - \frac{117059}{633623}e^{15} - \frac{195798}{633623}e^{14} + \frac{5573179}{1267246}e^{13} - \frac{3496015}{1267246}e^{12} - \frac{24254939}{633623}e^{11} + \frac{73432975}{1267246}e^{10} + \frac{91952381}{633623}e^{9} - \frac{203395223}{633623}e^{8} - \frac{273280073}{1267246}e^{7} + \frac{946943633}{1267246}e^{6} + \frac{86369425}{1267246}e^{5} - \frac{492091799}{633623}e^{4} + \frac{41668927}{1267246}e^{3} + \frac{210029898}{633623}e^{2} + \frac{10787330}{633623}e - \frac{18738699}{633623}$ |
| 67 | $[67, 67, w - 5]$ | $-\frac{631243}{1900869}e^{16} + \frac{7615813}{7603476}e^{15} + \frac{15651085}{1900869}e^{14} - \frac{200667991}{7603476}e^{13} - \frac{582742567}{7603476}e^{12} + \frac{2050987433}{7603476}e^{11} + \frac{416993911}{1267246}e^{10} - \frac{5140451591}{3801738}e^{9} - \frac{4912912225}{7603476}e^{8} + \frac{13316011073}{3801738}e^{7} + \frac{324580105}{633623}e^{6} - \frac{35271207559}{7603476}e^{5} - \frac{178368658}{1900869}e^{4} + \frac{1769738040}{633623}e^{3} - \frac{156434177}{3801738}e^{2} - \frac{901844935}{1900869}e + \frac{48434146}{633623}$ |
| 71 | $[71, 71, w^{2} - 2w - 11]$ | $-\frac{635089}{1267246}e^{16} + \frac{4981855}{2534492}e^{15} + \frac{14354601}{1267246}e^{14} - \frac{130095149}{2534492}e^{13} - \frac{222395679}{2534492}e^{12} + \frac{1314719829}{2534492}e^{11} + \frac{143757630}{633623}e^{10} - \frac{3251679885}{1267246}e^{9} + \frac{648328121}{2534492}e^{8} + \frac{8330390087}{1267246}e^{7} - \frac{1220591136}{633623}e^{6} - \frac{22195347593}{2534492}e^{5} + \frac{1584346591}{633623}e^{4} + \frac{6945009841}{1267246}e^{3} - \frac{1174949437}{1267246}e^{2} - \frac{600135577}{633623}e + \frac{128760294}{633623}$ |
| 73 | $[73, 73, w^{2} + 1]$ | $\phantom{-}\frac{1171775}{1900869}e^{16} - \frac{4036676}{1900869}e^{15} - \frac{54645265}{3801738}e^{14} + \frac{208818241}{3801738}e^{13} + \frac{454909825}{3801738}e^{12} - \frac{1039699429}{1900869}e^{11} - \frac{253376622}{633623}e^{10} + \frac{10045772089}{3801738}e^{9} + \frac{550158887}{1900869}e^{8} - \frac{24777132325}{3801738}e^{7} + \frac{1096999607}{1267246}e^{6} + \frac{15631692071}{1900869}e^{5} - \frac{5178030743}{3801738}e^{4} - \frac{6097925305}{1267246}e^{3} + \frac{853590641}{1900869}e^{2} + \frac{1461359189}{1900869}e - \frac{86024126}{633623}$ |
| 83 | $[83, 83, -4w^{2} + 3w + 27]$ | $\phantom{-}\frac{6813}{633623}e^{16} - \frac{115433}{633623}e^{15} + \frac{72552}{633623}e^{14} + \frac{5605213}{1267246}e^{13} - \frac{8843255}{1267246}e^{12} - \frac{25365018}{633623}e^{11} + \frac{98194599}{1267246}e^{10} + \frac{105140054}{633623}e^{9} - \frac{227018798}{633623}e^{8} - \frac{201946284}{633623}e^{7} + \frac{932192347}{1267246}e^{6} + \frac{369161603}{1267246}e^{5} - \frac{791247201}{1267246}e^{4} - \frac{84132756}{633623}e^{3} + \frac{97542832}{633623}e^{2} - \frac{3082417}{633623}e - \frac{7619640}{633623}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{2} + 5]$ | $-1$ |