Base field 3.3.1129.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} + w + 4]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 30x^{12} + 8x^{11} + 329x^{10} - 175x^{9} - 1602x^{8} + 1255x^{7} + 3262x^{6} - 3415x^{5} - 1605x^{4} + 2650x^{3} - 744x^{2} - 8x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{9028111661}{115289117408}e^{13} - \frac{1907258453}{57644558704}e^{12} + \frac{134605531889}{57644558704}e^{11} + \frac{10479091471}{28822279352}e^{10} - \frac{2950583297437}{115289117408}e^{9} + \frac{321907883097}{115289117408}e^{8} + \frac{3640427020883}{28822279352}e^{7} - \frac{5055938038387}{115289117408}e^{6} - \frac{7831853709287}{28822279352}e^{5} + \frac{17004131629123}{115289117408}e^{4} + \frac{21031540883095}{115289117408}e^{3} - \frac{3474031368921}{28822279352}e^{2} + \frac{70471169307}{7205569838}e + \frac{7071029893}{14411139676}$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{12904312733}{57644558704}e^{13} + \frac{2405167993}{28822279352}e^{12} - \frac{192468332349}{28822279352}e^{11} - \frac{10001552507}{14411139676}e^{10} + \frac{4219870264173}{57644558704}e^{9} - \frac{689132794625}{57644558704}e^{8} - \frac{5207249635083}{14411139676}e^{7} + \frac{8443037500059}{57644558704}e^{6} + \frac{11212637902365}{14411139676}e^{5} - \frac{27347634665211}{57644558704}e^{4} - \frac{30305133927951}{57644558704}e^{3} + \frac{5739221784653}{14411139676}e^{2} - \frac{169875131613}{7205569838}e - \frac{92269231367}{7205569838}$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{17397364377}{57644558704}e^{13} + \frac{3154357589}{28822279352}e^{12} - \frac{259432951445}{28822279352}e^{11} - \frac{12035621523}{14411139676}e^{10} + \frac{5684375261273}{57644558704}e^{9} - \frac{1001804405421}{57644558704}e^{8} - \frac{7001657384413}{14411139676}e^{7} + \frac{11811615053415}{57644558704}e^{6} + \frac{14995241540321}{14411139676}e^{5} - \frac{37986553568823}{57644558704}e^{4} - \frac{39566454233443}{57644558704}e^{3} + \frac{7926916614071}{14411139676}e^{2} - \frac{177263608645}{3602784919}e - \frac{83327836587}{7205569838}$ |
| 11 | $[11, 11, -w^{2} + 5]$ | $-\frac{18409573371}{115289117408}e^{13} - \frac{4847857823}{57644558704}e^{12} + \frac{273389557599}{57644558704}e^{11} + \frac{34771295893}{28822279352}e^{10} - \frac{5975306851179}{115289117408}e^{9} + \frac{115264376631}{115289117408}e^{8} + \frac{7377151683171}{28822279352}e^{7} - \frac{7927852220325}{115289117408}e^{6} - \frac{16056629573275}{28822279352}e^{5} + \frac{30474203069077}{115289117408}e^{4} + \frac{45890990108041}{115289117408}e^{3} - \frac{6721345128093}{28822279352}e^{2} - \frac{33042336911}{7205569838}e + \frac{95628138503}{14411139676}$ |
| 13 | $[13, 13, w^{2} - w - 7]$ | $\phantom{-}\frac{40578477861}{115289117408}e^{13} + \frac{6584280729}{57644558704}e^{12} - \frac{607006390921}{57644558704}e^{11} - \frac{18225560763}{28822279352}e^{10} + \frac{13350477494005}{115289117408}e^{9} - \frac{2682809286073}{115289117408}e^{8} - \frac{16524552402261}{28822279352}e^{7} + \frac{28785261391115}{115289117408}e^{6} + \frac{35659829233657}{28822279352}e^{5} - \frac{90195798286427}{115289117408}e^{4} - \frac{96089778873767}{115289117408}e^{3} + \frac{18616360423891}{28822279352}e^{2} - \frac{168540750441}{3602784919}e - \frac{235252825109}{14411139676}$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $-1$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $-\frac{24152480653}{57644558704}e^{13} - \frac{4939450585}{28822279352}e^{12} + \frac{359558708873}{28822279352}e^{11} + \frac{24674149887}{14411139676}e^{10} - \frac{7866586571709}{57644558704}e^{9} + \frac{1059376102897}{57644558704}e^{8} + \frac{9682970441469}{14411139676}e^{7} - \frac{14837717331347}{57644558704}e^{6} - \frac{20772911501081}{14411139676}e^{5} + \frac{49429076826211}{57644558704}e^{4} + \frac{55530633906815}{57644558704}e^{3} - \frac{10403763657255}{14411139676}e^{2} + \frac{199681764405}{3602784919}e + \frac{117971091457}{7205569838}$ |
| 29 | $[29, 29, 2w^{2} - 2w - 11]$ | $\phantom{-}\frac{4610458619}{14411139676}e^{13} + \frac{298224315}{3602784919}e^{12} - \frac{68862763039}{7205569838}e^{11} + \frac{444250839}{3602784919}e^{10} + \frac{1509920910579}{14411139676}e^{9} - \frac{427680470177}{14411139676}e^{8} - \frac{3713429155881}{7205569838}e^{7} + \frac{3943082601937}{14411139676}e^{6} + \frac{7883896203649}{7205569838}e^{5} - \frac{11832768533085}{14411139676}e^{4} - \frac{9925303196907}{14411139676}e^{3} + \frac{4814522256143}{7205569838}e^{2} - \frac{313019567846}{3602784919}e - \frac{62377177502}{3602784919}$ |
| 31 | $[31, 31, w^{2} - 2w - 4]$ | $-\frac{56475814873}{115289117408}e^{13} - \frac{5723103557}{57644558704}e^{12} + \frac{846629247157}{57644558704}e^{11} - \frac{26542910097}{28822279352}e^{10} - \frac{18641509267337}{115289117408}e^{9} + \frac{6040843572237}{115289117408}e^{8} + \frac{23035541524353}{28822279352}e^{7} - \frac{51626715150695}{115289117408}e^{6} - \frac{49243045707641}{28822279352}e^{5} + \frac{150941796220151}{115289117408}e^{4} + \frac{126510281019859}{115289117408}e^{3} - \frac{30495096493575}{28822279352}e^{2} + \frac{818739642325}{7205569838}e + \frac{350707378421}{14411139676}$ |
| 37 | $[37, 37, -2w^{2} + 3w + 7]$ | $\phantom{-}\frac{66835582663}{115289117408}e^{13} + \frac{9222426367}{57644558704}e^{12} - \frac{1001429190179}{57644558704}e^{11} - \frac{5209991341}{28822279352}e^{10} + \frac{22061413322711}{115289117408}e^{9} - \frac{5553037161035}{115289117408}e^{8} - \frac{27339851372657}{28822279352}e^{7} + \frac{53386143768377}{115289117408}e^{6} + \frac{58973861246965}{28822279352}e^{5} - \frac{162719430451337}{115289117408}e^{4} - \frac{157552188268517}{115289117408}e^{3} + \frac{33565853370259}{28822279352}e^{2} - \frac{619931528957}{7205569838}e - \frac{569999805527}{14411139676}$ |
| 41 | $[41, 41, w^{2} - 2]$ | $-\frac{28233094735}{57644558704}e^{13} - \frac{4486100345}{28822279352}e^{12} + \frac{422203704991}{28822279352}e^{11} + \frac{11075663479}{14411139676}e^{10} - \frac{9280340412575}{57644558704}e^{9} + \frac{1948063604335}{57644558704}e^{8} + \frac{5736759289323}{7205569838}e^{7} - \frac{20512360462001}{57644558704}e^{6} - \frac{6176329287112}{3602784919}e^{5} + \frac{64144629144833}{57644558704}e^{4} + \frac{66265422392681}{57644558704}e^{3} - \frac{3343701437043}{3602784919}e^{2} + \frac{225187027020}{3602784919}e + \frac{199306033021}{7205569838}$ |
| 59 | $[59, 59, 2w^{2} - 13]$ | $\phantom{-}\frac{1161886343}{14411139676}e^{13} + \frac{329634322}{3602784919}e^{12} - \frac{17096443913}{7205569838}e^{11} - \frac{7389220994}{3602784919}e^{10} + \frac{373409179819}{14411139676}e^{9} + \frac{216445215831}{14411139676}e^{8} - \frac{941391003327}{7205569838}e^{7} - \frac{583042948487}{14411139676}e^{6} + \frac{2208663723199}{7205569838}e^{5} + \frac{396887998419}{14411139676}e^{4} - \frac{4125354077395}{14411139676}e^{3} + \frac{2084445311}{7205569838}e^{2} + \frac{246813716478}{3602784919}e + \frac{2706545220}{3602784919}$ |
| 61 | $[61, 61, w^{2} + w - 10]$ | $-\frac{26155103601}{57644558704}e^{13} - \frac{2505716709}{28822279352}e^{12} + \frac{391663149141}{28822279352}e^{11} - \frac{15170091233}{14411139676}e^{10} - \frac{8608476734577}{57644558704}e^{9} + \frac{2964595726069}{57644558704}e^{8} + \frac{10603647131609}{14411139676}e^{7} - \frac{24999949600511}{57644558704}e^{6} - \frac{22511464033885}{14411139676}e^{5} + \frac{73061151381215}{57644558704}e^{4} + \frac{56294375401755}{57644558704}e^{3} - \frac{14915610904987}{14411139676}e^{2} + \frac{484494459204}{3602784919}e + \frac{196556192545}{7205569838}$ |
| 67 | $[67, 67, 2w^{2} - w - 11]$ | $-\frac{37118059333}{115289117408}e^{13} - \frac{5725718593}{57644558704}e^{12} + \frac{557137667433}{57644558704}e^{11} + \frac{12234002779}{28822279352}e^{10} - \frac{12315029981845}{115289117408}e^{9} + \frac{2660733088425}{115289117408}e^{8} + \frac{15359459797817}{28822279352}e^{7} - \frac{27474815204427}{115289117408}e^{6} - \frac{33574725762005}{28822279352}e^{5} + \frac{85226255126331}{115289117408}e^{4} + \frac{93897142118935}{115289117408}e^{3} - \frac{17522906183815}{28822279352}e^{2} + \frac{32470218514}{3602784919}e + \frac{331000571885}{14411139676}$ |
| 73 | $[73, 73, -w^{2} - 1]$ | $-\frac{3331071197}{57644558704}e^{13} - \frac{1019192713}{28822279352}e^{12} + \frac{50304686449}{28822279352}e^{11} + \frac{9781266787}{14411139676}e^{10} - \frac{1125694512477}{57644558704}e^{9} - \frac{204171911535}{57644558704}e^{8} + \frac{1441235612301}{14411139676}e^{7} + \frac{87183210685}{57644558704}e^{6} - \frac{3355305701301}{14411139676}e^{5} + \frac{1282119161459}{57644558704}e^{4} + \frac{11523422576527}{57644558704}e^{3} - \frac{305316903539}{14411139676}e^{2} - \frac{95631594520}{3602784919}e - \frac{9788415839}{7205569838}$ |
| 83 | $[83, 83, w^{2} - w - 10]$ | $-\frac{20386895045}{28822279352}e^{13} - \frac{2412510395}{14411139676}e^{12} + \frac{305679727717}{14411139676}e^{11} - \frac{4549712793}{7205569838}e^{10} - \frac{6737606581365}{28822279352}e^{9} + \frac{1972191947581}{28822279352}e^{8} + \frac{4174919267942}{3602784919}e^{7} - \frac{17711176620355}{28822279352}e^{6} - \frac{8993790580343}{3602784919}e^{5} + \frac{52817411242467}{28822279352}e^{4} + \frac{47732159616203}{28822279352}e^{3} - \frac{5406170874432}{3602784919}e^{2} + \frac{395781935215}{3602784919}e + \frac{184700836851}{3602784919}$ |
| 89 | $[89, 89, -w^{2} + 4w - 2]$ | $\phantom{-}\frac{28031520077}{57644558704}e^{13} + \frac{4177762807}{28822279352}e^{12} - \frac{419874628573}{28822279352}e^{11} - \frac{6917509245}{14411139676}e^{10} + \frac{9245671589341}{57644558704}e^{9} - \frac{2119620257029}{57644558704}e^{8} - \frac{2861953895867}{3602784919}e^{7} + \frac{21380133338531}{57644558704}e^{6} + \frac{12315886955087}{7205569838}e^{5} - \frac{66247625679859}{57644558704}e^{4} - \frac{65024402977395}{57644558704}e^{3} + \frac{6908704747615}{7205569838}e^{2} - \frac{323260818475}{3602784919}e - \frac{215405186263}{7205569838}$ |
| 97 | $[97, 97, w^{2} - 2w - 7]$ | $-\frac{105431360533}{115289117408}e^{13} - \frac{17418864073}{57644558704}e^{12} + \frac{1574700517161}{57644558704}e^{11} + \frac{47546244179}{28822279352}e^{10} - \frac{34565622480773}{115289117408}e^{9} + \frac{7198950516329}{115289117408}e^{8} + \frac{42654494001317}{28822279352}e^{7} - \frac{77279345624251}{115289117408}e^{6} - \frac{91433686993025}{28822279352}e^{5} + \frac{242822540801963}{115289117408}e^{4} + \frac{239676503893431}{115289117408}e^{3} - \frac{50337177471851}{28822279352}e^{2} + \frac{621963131340}{3602784919}e + \frac{539038257949}{14411139676}$ |
| 97 | $[97, 97, -w^{2} - 4w - 5]$ | $-\frac{59328913189}{57644558704}e^{13} - \frac{8430395949}{28822279352}e^{12} + \frac{887443138689}{28822279352}e^{11} + \frac{7714799039}{14411139676}e^{10} - \frac{19503232738325}{57644558704}e^{9} + \frac{4810549845649}{57644558704}e^{8} + \frac{24079974022567}{14411139676}e^{7} - \frac{46805329387771}{57644558704}e^{6} - \frac{51590402553263}{14411139676}e^{5} + \frac{142851400565259}{57644558704}e^{4} + \frac{134956699395071}{57644558704}e^{3} - \frac{29270278627693}{14411139676}e^{2} + \frac{688790710871}{3602784919}e + \frac{354861284929}{7205569838}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} + w + 4]$ | $1$ |