Base field 4.4.15952.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ |
| Dimension: | $21$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{21} - 5x^{20} - 19x^{19} + 125x^{18} + 110x^{17} - 1294x^{16} + 81x^{15} + 7211x^{14} - 3631x^{13} - 23611x^{12} + 17397x^{11} + 46651x^{10} - 40136x^{9} - 54932x^{8} + 50361x^{7} + 36489x^{6} - 33877x^{5} - 12175x^{4} + 10879x^{3} + 1695x^{2} - 1160x - 132\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{3} + w^{2} + 5w - 2]$ | $-\frac{6164045801}{69076492302}e^{20} + \frac{686346065}{1817802429}e^{19} + \frac{133867043089}{69076492302}e^{18} - \frac{326823799999}{34538246151}e^{17} - \frac{556970894230}{34538246151}e^{16} + \frac{3395389645604}{34538246151}e^{15} + \frac{4233496691165}{69076492302}e^{14} - \frac{19023315165733}{34538246151}e^{13} - \frac{1835108679687}{23025497434}e^{12} + \frac{62812100875865}{34538246151}e^{11} - \frac{3325689811951}{23025497434}e^{10} - \frac{41924625333129}{11512748717}e^{9} + \frac{20890140678749}{34538246151}e^{8} + \frac{151332124291301}{34538246151}e^{7} - \frac{51253611392227}{69076492302}e^{6} - \frac{104070547861208}{34538246151}e^{5} + \frac{8434597468789}{23025497434}e^{4} + \frac{12127470519381}{11512748717}e^{3} - \frac{2954895219527}{69076492302}e^{2} - \frac{83220125316}{605934143}e - \frac{138616451434}{11512748717}$ |
| 11 | $[11, 11, -w^{3} + 5w + 1]$ | $-\frac{583245683}{69076492302}e^{20} + \frac{115350515}{1817802429}e^{19} + \frac{10776687649}{69076492302}e^{18} - \frac{61425273955}{34538246151}e^{17} - \frac{24001399546}{34538246151}e^{16} + \frac{724828106180}{34538246151}e^{15} - \frac{316276783339}{69076492302}e^{14} - \frac{4677162532576}{34538246151}e^{13} + \frac{1413627421409}{23025497434}e^{12} + \frac{17934495364847}{34538246151}e^{11} - \frac{6372214529029}{23025497434}e^{10} - \frac{13854354489566}{11512748717}e^{9} + \frac{22087690785179}{34538246151}e^{8} + \frac{56615728125188}{34538246151}e^{7} - \frac{54608496685039}{69076492302}e^{6} - \frac{41967409941242}{34538246151}e^{5} + \frac{11166937553737}{23025497434}e^{4} + \frac{4845120650944}{11512748717}e^{3} - \frac{7585908533297}{69076492302}e^{2} - \frac{29694804435}{605934143}e - \frac{6612810294}{11512748717}$ |
| 11 | $[11, 11, -w + 2]$ | $\phantom{-}\frac{2464279611}{23025497434}e^{20} - \frac{5777290287}{11512748717}e^{19} - \frac{53050457509}{23025497434}e^{18} + \frac{7892170271}{605934143}e^{17} + \frac{213794329078}{11512748717}e^{16} - \frac{1629120251421}{11512748717}e^{15} - \frac{1440115538303}{23025497434}e^{14} + \frac{9658186061674}{11512748717}e^{13} + \frac{404524650423}{23025497434}e^{12} - \frac{34178035375841}{11512748717}e^{11} + \frac{10982295438051}{23025497434}e^{10} + \frac{74142585836273}{11512748717}e^{9} - \frac{15875026175250}{11512748717}e^{8} - \frac{96998778465325}{11512748717}e^{7} + \frac{37669008587411}{23025497434}e^{6} + \frac{71758287130972}{11512748717}e^{5} - \frac{19486071987861}{23025497434}e^{4} - \frac{26121031883749}{11512748717}e^{3} + \frac{2761069520015}{23025497434}e^{2} + \frac{3330481250870}{11512748717}e + \frac{300488228586}{11512748717}$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 4w + 1]$ | $-\frac{1409686311}{23025497434}e^{20} + \frac{492944632}{1817802429}e^{19} + \frac{92816677679}{69076492302}e^{18} - \frac{240407195135}{34538246151}e^{17} - \frac{390512350676}{34538246151}e^{16} + \frac{2570843171704}{34538246151}e^{15} + \frac{2998354724405}{69076492302}e^{14} - \frac{14901063278431}{34538246151}e^{13} - \frac{3905392872043}{69076492302}e^{12} + \frac{17023667223636}{11512748717}e^{11} - \frac{7176572989639}{69076492302}e^{10} - \frac{35311790635784}{11512748717}e^{9} + \frac{4771048260313}{11512748717}e^{8} + \frac{130266232710934}{34538246151}e^{7} - \frac{30737535966727}{69076492302}e^{6} - \frac{88510632136630}{34538246151}e^{5} + \frac{10027753773757}{69076492302}e^{4} + \frac{9616679414083}{11512748717}e^{3} + \frac{314300768513}{23025497434}e^{2} - \frac{178667765219}{1817802429}e - \frac{84434656672}{11512748717}$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $-1$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}\frac{1284290887}{11512748717}e^{20} - \frac{5923646581}{11512748717}e^{19} - \frac{27697876720}{11512748717}e^{18} + \frac{152800325763}{11512748717}e^{17} + \frac{225405738858}{11512748717}e^{16} - \frac{1647987527671}{11512748717}e^{15} - \frac{794162696915}{11512748717}e^{14} + \frac{9689145198428}{11512748717}e^{13} + \frac{573941938040}{11512748717}e^{12} - \frac{33987536982034}{11512748717}e^{11} + \frac{4049259233101}{11512748717}e^{10} + \frac{73139244017682}{11512748717}e^{9} - \frac{12118803749511}{11512748717}e^{8} - \frac{95176701847519}{11512748717}e^{7} + \frac{13062126429002}{11512748717}e^{6} + \frac{70366012682823}{11512748717}e^{5} - \frac{272027290474}{605934143}e^{4} - \frac{25726130631720}{11512748717}e^{3} - \frac{67959207962}{11512748717}e^{2} + \frac{3334357714791}{11512748717}e + \frac{372418855194}{11512748717}$ |
| 23 | $[23, 23, w^{3} - 6w]$ | $-\frac{5969395343}{69076492302}e^{20} + \frac{11494061935}{34538246151}e^{19} + \frac{142724955635}{69076492302}e^{18} - \frac{300021167210}{34538246151}e^{17} - \frac{689116152998}{34538246151}e^{16} + \frac{3266708276542}{34538246151}e^{15} + \frac{2282897531151}{23025497434}e^{14} - \frac{6427468714576}{11512748717}e^{13} - \frac{18289621283381}{69076492302}e^{12} + \frac{67173977360195}{34538246151}e^{11} + \frac{1252698982195}{3635604858}e^{10} - \frac{46973882022553}{11512748717}e^{9} - \frac{3225977142712}{34538246151}e^{8} + \frac{173830223465623}{34538246151}e^{7} - \frac{5660539302975}{23025497434}e^{6} - \frac{117235009511692}{34538246151}e^{5} + \frac{17013356832029}{69076492302}e^{4} + \frac{12422075282002}{11512748717}e^{3} - \frac{4655329568855}{69076492302}e^{2} - \frac{3976198634101}{34538246151}e - \frac{54208757866}{11512748717}$ |
| 27 | $[27, 3, w^{3} + w^{2} - 5w - 4]$ | $-\frac{19124591179}{69076492302}e^{20} + \frac{37026955400}{34538246151}e^{19} + \frac{444737288767}{69076492302}e^{18} - \frac{945150201667}{34538246151}e^{17} - \frac{2079272161453}{34538246151}e^{16} + \frac{10041684051599}{34538246151}e^{15} + \frac{6659468905555}{23025497434}e^{14} - \frac{19262544811360}{11512748717}e^{13} - \frac{52198944758461}{69076492302}e^{12} + \frac{196692285007963}{34538246151}e^{11} + \frac{71683819084379}{69076492302}e^{10} - \frac{135388507955981}{11512748717}e^{9} - \frac{21713005922546}{34538246151}e^{8} + \frac{500443828999934}{34538246151}e^{7} + \frac{997698050841}{23025497434}e^{6} - \frac{344644807113428}{34538246151}e^{5} + \frac{3854887905997}{69076492302}e^{4} + \frac{38115150483635}{11512748717}e^{3} + \frac{2811792803219}{69076492302}e^{2} - \frac{12604312606175}{34538246151}e - \frac{405032235126}{11512748717}$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 5w]$ | $\phantom{-}\frac{11873991217}{34538246151}e^{20} - \frac{52014674905}{34538246151}e^{19} - \frac{261964031653}{34538246151}e^{18} + \frac{1339096960739}{34538246151}e^{17} + \frac{2218539077426}{34538246151}e^{16} - \frac{14389032289063}{34538246151}e^{15} - \frac{2851168373646}{11512748717}e^{14} + \frac{28020183591036}{11512748717}e^{13} + \frac{10631825091976}{34538246151}e^{12} - \frac{291877239744335}{34538246151}e^{11} + \frac{26428697914135}{34538246151}e^{10} + \frac{206252720890539}{11512748717}e^{9} - \frac{106869501618233}{34538246151}e^{8} - \frac{789438611045974}{34538246151}e^{7} + \frac{45767699441371}{11512748717}e^{6} + \frac{30039571779439}{1817802429}e^{5} - \frac{72319973478616}{34538246151}e^{4} - \frac{68140986745551}{11512748717}e^{3} + \frac{9707829455263}{34538246151}e^{2} + \frac{26065782603799}{34538246151}e + \frac{804650029102}{11512748717}$ |
| 41 | $[41, 41, 2w^{3} - 11w - 4]$ | $-\frac{16798500112}{34538246151}e^{20} + \frac{1296251505}{605934143}e^{19} + \frac{121273409324}{11512748717}e^{18} - \frac{625043545713}{11512748717}e^{17} - \frac{1001147766157}{11512748717}e^{16} + \frac{6601159304865}{11512748717}e^{15} + \frac{11137436516147}{34538246151}e^{14} - \frac{113344389680102}{34538246151}e^{13} - \frac{12577383026744}{34538246151}e^{12} + \frac{384441366035342}{34538246151}e^{11} - \frac{34633825525598}{34538246151}e^{10} - \frac{264857862530958}{11512748717}e^{9} + \frac{123749708330522}{34538246151}e^{8} + \frac{329284699342005}{11512748717}e^{7} - \frac{139981695371203}{34538246151}e^{6} - \frac{232246081528030}{11512748717}e^{5} + \frac{59050238402234}{34538246151}e^{4} + \frac{81690636111259}{11512748717}e^{3} - \frac{1627199487205}{34538246151}e^{2} - \frac{1665236885861}{1817802429}e - \frac{1095521858618}{11512748717}$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ | $\phantom{-}\frac{5586543661}{23025497434}e^{20} - \frac{642246058}{605934143}e^{19} - \frac{117578293945}{23025497434}e^{18} + \frac{303878715416}{11512748717}e^{17} + \frac{459190011150}{11512748717}e^{16} - \frac{3133312658866}{11512748717}e^{15} - \frac{2924731771701}{23025497434}e^{14} + \frac{17403690584797}{11512748717}e^{13} + \frac{125761662605}{23025497434}e^{12} - \frac{56924631049756}{11512748717}e^{11} + \frac{24115589294165}{23025497434}e^{10} + \frac{112895508410821}{11512748717}e^{9} - \frac{32882405534107}{11512748717}e^{8} - \frac{134499242318465}{11512748717}e^{7} + \frac{76916979425543}{23025497434}e^{6} + \frac{91227673579224}{11512748717}e^{5} - \frac{41211887581919}{23025497434}e^{4} - \frac{31033129601204}{11512748717}e^{3} + \frac{7483675702499}{23025497434}e^{2} + \frac{203396971626}{605934143}e + \frac{263598930120}{11512748717}$ |
| 59 | $[59, 59, 2w^{3} - 11w - 2]$ | $-\frac{5266942934}{34538246151}e^{20} + \frac{1196622734}{1817802429}e^{19} + \frac{112510643051}{34538246151}e^{18} - \frac{565835684884}{34538246151}e^{17} - \frac{911754175462}{34538246151}e^{16} + \frac{5823166118348}{34538246151}e^{15} + \frac{1097447792691}{11512748717}e^{14} - \frac{10732719861348}{11512748717}e^{13} - \frac{3526375462571}{34538246151}e^{12} + \frac{104312937676132}{34538246151}e^{11} - \frac{9836468766662}{34538246151}e^{10} - \frac{67668168961316}{11512748717}e^{9} + \frac{32526352347031}{34538246151}e^{8} + \frac{233456823500504}{34538246151}e^{7} - \frac{11065382800594}{11512748717}e^{6} - \frac{148727268344318}{34538246151}e^{5} + \frac{11187510003470}{34538246151}e^{4} + \frac{15150769063434}{11512748717}e^{3} + \frac{671462896114}{34538246151}e^{2} - \frac{248876236814}{1817802429}e - \frac{174463959092}{11512748717}$ |
| 67 | $[67, 67, w^{3} - 7w - 1]$ | $-\frac{8605377185}{34538246151}e^{20} + \frac{42713630768}{34538246151}e^{19} + \frac{176116887824}{34538246151}e^{18} - \frac{1094418317164}{34538246151}e^{17} - \frac{1284855435037}{34538246151}e^{16} + \frac{11713185423836}{34538246151}e^{15} + \frac{1045867958128}{11512748717}e^{14} - \frac{22762003549308}{11512748717}e^{13} + \frac{7262862750829}{34538246151}e^{12} + \frac{237445144748752}{34538246151}e^{11} - \frac{59257683419465}{34538246151}e^{10} - \frac{168894198560298}{11512748717}e^{9} + \frac{135075979213066}{34538246151}e^{8} + \frac{654080451437690}{34538246151}e^{7} - \frac{46467421165679}{11512748717}e^{6} - \frac{479317831485002}{34538246151}e^{5} + \frac{62515950631496}{34538246151}e^{4} + \frac{57802174495544}{11512748717}e^{3} - \frac{7313506324607}{34538246151}e^{2} - \frac{22290274905422}{34538246151}e - \frac{572437003540}{11512748717}$ |
| 71 | $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ | $-\frac{11843851735}{34538246151}e^{20} + \frac{14430235493}{11512748717}e^{19} + \frac{94989137651}{11512748717}e^{18} - \frac{371149104608}{11512748717}e^{17} - \frac{935366147392}{11512748717}e^{16} + \frac{3980012786016}{11512748717}e^{15} + \frac{14645701860347}{34538246151}e^{14} - \frac{69500852837825}{34538246151}e^{13} - \frac{44084117845790}{34538246151}e^{12} + \frac{239911383987239}{34538246151}e^{11} + \frac{78759332010169}{34538246151}e^{10} - \frac{168045997429420}{11512748717}e^{9} - \frac{84003784095238}{34538246151}e^{8} + \frac{211715601322367}{11512748717}e^{7} + \frac{53601080665388}{34538246151}e^{6} - \frac{7904497629486}{605934143}e^{5} - \frac{20560594346479}{34538246151}e^{4} + \frac{51847324454469}{11512748717}e^{3} + \frac{5130774586565}{34538246151}e^{2} - \frac{18171756031271}{34538246151}e - \frac{481112395280}{11512748717}$ |
| 79 | $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ | $\phantom{-}\frac{28822702025}{69076492302}e^{20} - \frac{53623256164}{34538246151}e^{19} - \frac{691148022989}{69076492302}e^{18} + \frac{1387421014988}{34538246151}e^{17} + \frac{177621523724}{1817802429}e^{16} - \frac{14986900325923}{34538246151}e^{15} - \frac{11527548358627}{23025497434}e^{14} + \frac{29337655471917}{11512748717}e^{13} + \frac{5263553728715}{3635604858}e^{12} - \frac{307057952556317}{34538246151}e^{11} - \frac{163920123628315}{69076492302}e^{10} + \frac{11464556747267}{605934143}e^{9} + \frac{72867463551691}{34538246151}e^{8} - \frac{44036547980374}{1817802429}e^{7} - \frac{22140645636115}{23025497434}e^{6} + \frac{608515569441451}{34538246151}e^{5} + \frac{22512708021229}{69076492302}e^{4} - \frac{73761176088358}{11512748717}e^{3} - \frac{15737639408365}{69076492302}e^{2} + \frac{29349402102304}{34538246151}e + \frac{1132847997614}{11512748717}$ |
| 89 | $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ | $\phantom{-}\frac{463392313}{1817802429}e^{20} - \frac{10203961223}{11512748717}e^{19} - \frac{71383723795}{11512748717}e^{18} + \frac{260709858491}{11512748717}e^{17} + \frac{714710276152}{11512748717}e^{16} - \frac{2770509178707}{11512748717}e^{15} - \frac{11488659113447}{34538246151}e^{14} + \frac{47773995782750}{34538246151}e^{13} + \frac{36078914782907}{34538246151}e^{12} - \frac{162004557030926}{34538246151}e^{11} - \frac{68999302300279}{34538246151}e^{10} + \frac{110659460532984}{11512748717}e^{9} + \frac{81671662297546}{34538246151}e^{8} - \frac{134636937545667}{11512748717}e^{7} - \frac{60178433483231}{34538246151}e^{6} + \frac{91212705050234}{11512748717}e^{5} + \frac{27728978305021}{34538246151}e^{4} - \frac{29791576594074}{11512748717}e^{3} - \frac{8026795784045}{34538246151}e^{2} + \frac{9656459537108}{34538246151}e + \frac{459554300366}{11512748717}$ |
| 101 | $[101, 101, -2w^{3} + 13w + 6]$ | $\phantom{-}\frac{24061596817}{34538246151}e^{20} - \frac{99435497869}{34538246151}e^{19} - \frac{538897209316}{34538246151}e^{18} + \frac{2526634584272}{34538246151}e^{17} + \frac{4728661242815}{34538246151}e^{16} - \frac{26706524366770}{34538246151}e^{15} - \frac{6704164224168}{11512748717}e^{14} + \frac{50951151593523}{11512748717}e^{13} + \frac{39177262715158}{34538246151}e^{12} - \frac{517634808050264}{34538246151}e^{11} - \frac{10429753669427}{34538246151}e^{10} + \frac{355167539171315}{11512748717}e^{9} - \frac{83459399029469}{34538246151}e^{8} - \frac{1314838445495116}{34538246151}e^{7} + \frac{2233769222687}{605934143}e^{6} + \frac{916682821907101}{34538246151}e^{5} - \frac{64257573225283}{34538246151}e^{4} - \frac{105533023767591}{11512748717}e^{3} + \frac{4872126455578}{34538246151}e^{2} + \frac{39521855315227}{34538246151}e + \frac{1156158358942}{11512748717}$ |
| 101 | $[101, 101, w^{3} + w^{2} - 6w - 3]$ | $\phantom{-}\frac{23718502289}{69076492302}e^{20} - \frac{39854909495}{34538246151}e^{19} - \frac{573117289771}{69076492302}e^{18} + \frac{1000929270625}{34538246151}e^{17} + \frac{2847421526689}{34538246151}e^{16} - \frac{10410602320721}{34538246151}e^{15} - \frac{30244814644565}{69076492302}e^{14} + \frac{58289551089028}{34538246151}e^{13} + \frac{31295245660001}{23025497434}e^{12} - \frac{191760669258356}{34538246151}e^{11} - \frac{58611850317619}{23025497434}e^{10} + \frac{127006889326511}{11512748717}e^{9} + \frac{98539137421672}{34538246151}e^{8} - \frac{453376281680699}{34538246151}e^{7} - \frac{123827898547169}{69076492302}e^{6} + \frac{308471751596141}{34538246151}e^{5} + \frac{12480688592251}{23025497434}e^{4} - \frac{35619902981562}{11512748717}e^{3} - \frac{5693946532033}{69076492302}e^{2} + \frac{4628283784902}{11512748717}e + \frac{354982166040}{11512748717}$ |
| 101 | $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ | $\phantom{-}\frac{10147446131}{34538246151}e^{20} - \frac{43172016643}{34538246151}e^{19} - \frac{227450945257}{34538246151}e^{18} + \frac{1109784262982}{34538246151}e^{17} + \frac{1990147231478}{34538246151}e^{16} - \frac{11900832775201}{34538246151}e^{15} - \frac{8341563294065}{34538246151}e^{14} + \frac{69329753981153}{34538246151}e^{13} + \frac{5062083443805}{11512748717}e^{12} - \frac{239779553750893}{34538246151}e^{11} + \frac{485031445819}{11512748717}e^{10} + \frac{168489319664307}{11512748717}e^{9} - \frac{47833340961010}{34538246151}e^{8} - \frac{639854980937437}{34538246151}e^{7} + \frac{66099365891071}{34538246151}e^{6} + \frac{458230285401931}{34538246151}e^{5} - \frac{542489046245}{605934143}e^{4} - \frac{54569571885949}{11512748717}e^{3} + \frac{1101041763371}{34538246151}e^{2} + \frac{7263718086308}{11512748717}e + \frac{729061680546}{11512748717}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $1$ |