Base field 5.5.138136.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 3x^{2} + 4x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ |
| Dimension: | $19$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $43$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{19} + 3x^{18} - 23x^{17} - 71x^{16} + 214x^{15} + 687x^{14} - 1037x^{13} - 3510x^{12} + 2823x^{11} + 10223x^{10} - 4413x^{9} - 17168x^{8} + 4009x^{7} + 16113x^{6} - 2071x^{5} - 7672x^{4} + 504x^{3} + 1439x^{2} - 32x - 15\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -2w^{4} + w^{3} + 12w^{2} + w - 5]$ | $\phantom{-}\frac{5049336}{253002341}e^{18} + \frac{76703640}{253002341}e^{17} + \frac{35997139}{253002341}e^{16} - \frac{1714879205}{253002341}e^{15} - \frac{2261674122}{253002341}e^{14} + \frac{15259431476}{253002341}e^{13} + \frac{24025396729}{253002341}e^{12} - \frac{68705112587}{253002341}e^{11} - \frac{115759652731}{253002341}e^{10} + \frac{164444677432}{253002341}e^{9} + \frac{286448216629}{253002341}e^{8} - \frac{201485592507}{253002341}e^{7} - \frac{359626053207}{253002341}e^{6} + \frac{110375209049}{253002341}e^{5} + \frac{209901867544}{253002341}e^{4} - \frac{11104114860}{253002341}e^{3} - \frac{43694742965}{253002341}e^{2} - \frac{6459263977}{253002341}e + \frac{97853167}{253002341}$ |
| 8 | $[8, 2, w^{4} - 7w^{2} - 3w + 5]$ | $\phantom{-}\frac{121433384}{253002341}e^{18} + \frac{557294486}{253002341}e^{17} - \frac{2080167705}{253002341}e^{16} - \frac{12345981170}{253002341}e^{15} + \frac{10199040003}{253002341}e^{14} + \frac{108813682933}{253002341}e^{13} + \frac{13353967165}{253002341}e^{12} - \frac{485273187773}{253002341}e^{11} - \frac{280222053156}{253002341}e^{10} + \frac{1152079307746}{253002341}e^{9} + \frac{953230704862}{253002341}e^{8} - \frac{1413779836219}{253002341}e^{7} - \frac{1365408087636}{253002341}e^{6} + \frac{825934062873}{253002341}e^{5} + \frac{858789001543}{253002341}e^{4} - \frac{178276435998}{253002341}e^{3} - \frac{194367778213}{253002341}e^{2} + \frac{2168345058}{253002341}e + \frac{2633397762}{253002341}$ |
| 19 | $[19, 19, -2w^{4} + w^{3} + 12w^{2} - 5]$ | $\phantom{-}\frac{83230600}{253002341}e^{18} + \frac{266074599}{253002341}e^{17} - \frac{1719250484}{253002341}e^{16} - \frac{5903524349}{253002341}e^{15} + \frac{13495928547}{253002341}e^{14} + \frac{52285361142}{253002341}e^{13} - \frac{48494500690}{253002341}e^{12} - \frac{235745098967}{253002341}e^{11} + \frac{68542882035}{253002341}e^{10} + \frac{572353301305}{253002341}e^{9} + \frac{17802244594}{253002341}e^{8} - \frac{734320104700}{253002341}e^{7} - \frac{118749760998}{253002341}e^{6} + \frac{467047440868}{253002341}e^{5} + \frac{78730052001}{253002341}e^{4} - \frac{121240569850}{253002341}e^{3} - \frac{13365002516}{253002341}e^{2} + \frac{6947070451}{253002341}e + \frac{34159444}{253002341}$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 5w - 1]$ | $\phantom{-}\frac{115961544}{253002341}e^{18} + \frac{522332198}{253002341}e^{17} - \frac{2026838654}{253002341}e^{16} - \frac{11601385551}{253002341}e^{15} + \frac{10648877492}{253002341}e^{14} + \frac{102681511679}{253002341}e^{13} + \frac{4655457144}{253002341}e^{12} - \frac{461174088313}{253002341}e^{11} - \frac{231490992844}{253002341}e^{10} + \frac{1108692822906}{253002341}e^{9} + \frac{826103799830}{253002341}e^{8} - \frac{1393523699952}{253002341}e^{7} - \frac{1205509545131}{253002341}e^{6} + \frac{855459504584}{253002341}e^{5} + \frac{766758654873}{253002341}e^{4} - \frac{212521369185}{253002341}e^{3} - \frac{172529384461}{253002341}e^{2} + \frac{11191591019}{253002341}e + \frac{744687262}{253002341}$ |
| 29 | $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ | $-1$ |
| 31 | $[31, 31, -2w^{4} + w^{3} + 12w^{2} + 2w - 5]$ | $-\frac{114809589}{253002341}e^{18} - \frac{486234469}{253002341}e^{17} + \frac{2067998529}{253002341}e^{16} + \frac{10736277060}{253002341}e^{15} - \frac{11926060571}{253002341}e^{14} - \frac{94178524685}{253002341}e^{13} + \frac{8004549859}{253002341}e^{12} + \frac{416883803857}{253002341}e^{11} + \frac{169510216647}{253002341}e^{10} - \frac{976540711048}{253002341}e^{9} - \frac{661850711576}{253002341}e^{8} + \frac{1164324311149}{253002341}e^{7} + \frac{971860811211}{253002341}e^{6} - \frac{629585415032}{253002341}e^{5} - \frac{603811090528}{253002341}e^{4} + \frac{95668586341}{253002341}e^{3} + \frac{131783130635}{253002341}e^{2} + \frac{13548141234}{253002341}e - \frac{1650411140}{253002341}$ |
| 37 | $[37, 37, -2w^{4} + 13w^{2} + 5w - 7]$ | $-\frac{178856108}{253002341}e^{18} - \frac{634617364}{253002341}e^{17} + \frac{3560949468}{253002341}e^{16} + \frac{14134671664}{253002341}e^{15} - \frac{25989737792}{253002341}e^{14} - \frac{125764561811}{253002341}e^{13} + \frac{76696907624}{253002341}e^{12} + \frac{570322452675}{253002341}e^{11} - \frac{16485438053}{253002341}e^{10} - \frac{1395431277827}{253002341}e^{9} - \frac{383240033178}{253002341}e^{8} + \frac{1811846035896}{253002341}e^{7} + \frac{750795546727}{253002341}e^{6} - \frac{1180021753032}{253002341}e^{5} - \frac{519471547226}{253002341}e^{4} + \frac{331763514017}{253002341}e^{3} + \frac{117949115461}{253002341}e^{2} - \frac{26808124059}{253002341}e - \frac{1388786564}{253002341}$ |
| 53 | $[53, 53, 3w^{4} - 2w^{3} - 18w^{2} + 3w + 9]$ | $-\frac{220161915}{253002341}e^{18} - \frac{939975717}{253002341}e^{17} + \frac{3960936956}{253002341}e^{16} + \frac{20842552856}{253002341}e^{15} - \frac{22749618325}{253002341}e^{14} - \frac{184056594947}{253002341}e^{13} + \frac{14196633654}{253002341}e^{12} + \frac{823965245727}{253002341}e^{11} + \frac{330272622731}{253002341}e^{10} - \frac{1970506759052}{253002341}e^{9} - \frac{1280275879821}{253002341}e^{8} + \frac{2451985087875}{253002341}e^{7} + \frac{1872115492458}{253002341}e^{6} - \frac{1466966405364}{253002341}e^{5} - \frac{1154858388068}{253002341}e^{4} + \frac{324182394347}{253002341}e^{3} + \frac{245814276530}{253002341}e^{2} - \frac{470082781}{253002341}e - \frac{259321398}{253002341}$ |
| 59 | $[59, 59, 2w^{4} - 13w^{2} - 6w + 5]$ | $-\frac{610078999}{253002341}e^{18} - \frac{2574406019}{253002341}e^{17} + \frac{11087287100}{253002341}e^{16} + \frac{57170170969}{253002341}e^{15} - \frac{65425853789}{253002341}e^{14} - \frac{505969327805}{253002341}e^{13} + \frac{59323846140}{253002341}e^{12} + \frac{2272896898415}{253002341}e^{11} + \frac{833077606332}{253002341}e^{10} - \frac{5468647680724}{253002341}e^{9} - \frac{3379048865928}{253002341}e^{8} + \frac{6889701287409}{253002341}e^{7} + \frac{5034936825400}{253002341}e^{6} - \frac{4251379570159}{253002341}e^{5} - \frac{3165342905287}{253002341}e^{4} + \frac{1056890601126}{253002341}e^{3} + \frac{699673328322}{253002341}e^{2} - \frac{49558005693}{253002341}e - \frac{7362089202}{253002341}$ |
| 61 | $[61, 61, -3w^{4} + 2w^{3} + 18w^{2} - 2w - 11]$ | $\phantom{-}\frac{656326698}{253002341}e^{18} + \frac{2809747533}{253002341}e^{17} - \frac{11708050728}{253002341}e^{16} - \frac{62203548919}{253002341}e^{15} + \frac{65374420740}{253002341}e^{14} + \frac{548107015868}{253002341}e^{13} - \frac{17923492716}{253002341}e^{12} - \frac{2446130000981}{253002341}e^{11} - \frac{1112140330127}{253002341}e^{10} + \frac{5824800717739}{253002341}e^{9} + \frac{4189540027502}{253002341}e^{8} - \frac{7213857307180}{253002341}e^{7} - \frac{6182435319266}{253002341}e^{6} + \frac{4333851340936}{253002341}e^{5} + \frac{3932747925746}{253002341}e^{4} - \frac{1034928843131}{253002341}e^{3} - \frac{888595913252}{253002341}e^{2} + \frac{42991527255}{253002341}e + \frac{7148804197}{253002341}$ |
| 61 | $[61, 61, w^{2} - w - 3]$ | $-\frac{408257912}{253002341}e^{18} - \frac{1667930390}{253002341}e^{17} + \frac{7467557265}{253002341}e^{16} + \frac{36909149814}{253002341}e^{15} - \frac{44689386084}{253002341}e^{14} - \frac{325114553764}{253002341}e^{13} + \frac{45891394927}{253002341}e^{12} + \frac{1450664292335}{253002341}e^{11} + \frac{540960102506}{253002341}e^{10} - \frac{3453921899155}{253002341}e^{9} - \frac{2261613423050}{253002341}e^{8} + \frac{4274042926476}{253002341}e^{7} + \frac{3449370999772}{253002341}e^{6} - \frac{2553612483570}{253002341}e^{5} - \frac{2240271627885}{253002341}e^{4} + \frac{592575536659}{253002341}e^{3} + \frac{519155220741}{253002341}e^{2} - \frac{17454780154}{253002341}e - \frac{7856052629}{253002341}$ |
| 61 | $[61, 61, 6w^{4} - 2w^{3} - 38w^{2} - 6w + 23]$ | $\phantom{-}\frac{250981625}{253002341}e^{18} + \frac{1129603690}{253002341}e^{17} - \frac{4291456672}{253002341}e^{16} - \frac{24878184962}{253002341}e^{15} + \frac{20958811862}{253002341}e^{14} + \frac{217528314541}{253002341}e^{13} + \frac{27950834193}{253002341}e^{12} - \frac{959011493388}{253002341}e^{11} - \frac{575840800577}{253002341}e^{10} + \frac{2236196043322}{253002341}e^{9} + \frac{1944166080352}{253002341}e^{8} - \frac{2661174701066}{253002341}e^{7} - \frac{2756283791298}{253002341}e^{6} + \frac{1469337035719}{253002341}e^{5} + \frac{1711324150863}{253002341}e^{4} - \frac{269557318226}{253002341}e^{3} - \frac{381630489445}{253002341}e^{2} - \frac{12242178565}{253002341}e + \frac{4617576226}{253002341}$ |
| 67 | $[67, 67, -w^{4} + 7w^{2} + 4w - 5]$ | $-\frac{714436036}{253002341}e^{18} - \frac{2834403091}{253002341}e^{17} + \frac{13223122607}{253002341}e^{16} + \frac{62574315197}{253002341}e^{15} - \frac{81654898043}{253002341}e^{14} - \frac{549330461861}{253002341}e^{13} + \frac{111119198982}{253002341}e^{12} + \frac{2438240493992}{253002341}e^{11} + \frac{805184449774}{253002341}e^{10} - \frac{5751981530540}{253002341}e^{9} - \frac{3602652077772}{253002341}e^{8} + \frac{6987441641162}{253002341}e^{7} + \frac{5555553874799}{253002341}e^{6} - \frac{4001520760861}{253002341}e^{5} - \frac{3591937285105}{253002341}e^{4} + \frac{812280337287}{253002341}e^{3} + \frac{815332281360}{253002341}e^{2} + \frac{9453348937}{253002341}e - \frac{8779241048}{253002341}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 1]$ | $-\frac{5922557}{253002341}e^{18} - \frac{216982654}{253002341}e^{17} - \frac{318992105}{253002341}e^{16} + \frac{4921447697}{253002341}e^{15} + \frac{8761082602}{253002341}e^{14} - \frac{44600154040}{253002341}e^{13} - \frac{81864355022}{253002341}e^{12} + \frac{205928534473}{253002341}e^{11} + \frac{374806562348}{253002341}e^{10} - \frac{512678299586}{253002341}e^{9} - \frac{902652845370}{253002341}e^{8} + \frac{676152768433}{253002341}e^{7} + \frac{1112387636030}{253002341}e^{6} - \frac{441640976020}{253002341}e^{5} - \frac{636562190525}{253002341}e^{4} + \frac{112039753731}{253002341}e^{3} + \frac{127642354952}{253002341}e^{2} - \frac{2754748656}{253002341}e + \frac{978091993}{253002341}$ |
| 71 | $[71, 71, -w^{2} + 3]$ | $\phantom{-}\frac{850622040}{253002341}e^{18} + \frac{3427730122}{253002341}e^{17} - \frac{15847224642}{253002341}e^{16} - \frac{76162126054}{253002341}e^{15} + \frac{99621744885}{253002341}e^{14} + \frac{674799332145}{253002341}e^{13} - \frac{154385283563}{253002341}e^{12} - \frac{3037364482999}{253002341}e^{11} - \frac{856464376008}{253002341}e^{10} + \frac{7332465631254}{253002341}e^{9} + \frac{4038679833774}{253002341}e^{8} - \frac{9283984791194}{253002341}e^{7} - \frac{6296174209166}{253002341}e^{6} + \frac{5754675315762}{253002341}e^{5} + \frac{4081996890352}{253002341}e^{4} - \frac{1421551547238}{253002341}e^{3} - \frac{929487838162}{253002341}e^{2} + \frac{57316988138}{253002341}e + \frac{8847755754}{253002341}$ |
| 73 | $[73, 73, 3w^{4} - w^{3} - 19w^{2} - 3w + 9]$ | $\phantom{-}\frac{721484080}{253002341}e^{18} + \frac{2833234875}{253002341}e^{17} - \frac{13460090670}{253002341}e^{16} - \frac{62617370710}{253002341}e^{15} + \frac{84828215014}{253002341}e^{14} + \frac{550671712308}{253002341}e^{13} - \frac{133118642942}{253002341}e^{12} - \frac{2451501320847}{253002341}e^{11} - \frac{720176797423}{253002341}e^{10} + \frac{5815806834740}{253002341}e^{9} + \frac{3420725598331}{253002341}e^{8} - \frac{7150681127466}{253002341}e^{7} - \frac{5355485880000}{253002341}e^{6} + \frac{4222557807078}{253002341}e^{5} + \frac{3496350331616}{253002341}e^{4} - \frac{961421829376}{253002341}e^{3} - \frac{802418118058}{253002341}e^{2} + \frac{27036825946}{253002341}e + \frac{8368449142}{253002341}$ |
| 79 | $[79, 79, 3w^{4} - w^{3} - 19w^{2} - 4w + 11]$ | $-\frac{699630746}{253002341}e^{18} - \frac{3042928204}{253002341}e^{17} + \frac{12411297014}{253002341}e^{16} + \frac{67411965540}{253002341}e^{15} - \frac{68233498754}{253002341}e^{14} - \frac{594411795535}{253002341}e^{13} + \frac{6976606543}{253002341}e^{12} + \frac{2654180355074}{253002341}e^{11} + \frac{1236789703003}{253002341}e^{10} - \frac{6318634902477}{253002341}e^{9} - \frac{4582233391681}{253002341}e^{8} + \frac{7798322686888}{253002341}e^{7} + \frac{6730327600023}{253002341}e^{6} - \frac{4605835737559}{253002341}e^{5} - \frac{4280985061368}{253002341}e^{4} + \frac{1012338441589}{253002341}e^{3} + \frac{978077182421}{253002341}e^{2} - \frac{9546529686}{253002341}e - \frac{12088219109}{253002341}$ |
| 83 | $[83, 83, -w^{4} - w^{3} + 7w^{2} + 8w - 3]$ | $-\frac{392655799}{253002341}e^{18} - \frac{1890879248}{253002341}e^{17} + \frac{6556989203}{253002341}e^{16} + \frac{42001258796}{253002341}e^{15} - \frac{29276663388}{253002341}e^{14} - \frac{371555849900}{253002341}e^{13} - \frac{75518158617}{253002341}e^{12} + \frac{1666066639783}{253002341}e^{11} + \frac{1049989974623}{253002341}e^{10} - \frac{3990019250524}{253002341}e^{9} - \frac{3426420624933}{253002341}e^{8} + \frac{4971310742828}{253002341}e^{7} + \frac{4844824919778}{253002341}e^{6} - \frac{2985141282129}{253002341}e^{5} - \frac{3030667467976}{253002341}e^{4} + \frac{683091590754}{253002341}e^{3} + \frac{679807634831}{253002341}e^{2} - \frac{15516757811}{253002341}e - \frac{6889877463}{253002341}$ |
| 97 | $[97, 97, -2w^{4} + w^{3} + 12w^{2} + 2w - 3]$ | $-\frac{169451304}{253002341}e^{18} - \frac{1000500613}{253002341}e^{17} + \frac{2316857958}{253002341}e^{16} + \frac{22106772551}{253002341}e^{15} - \frac{1325253566}{253002341}e^{14} - \frac{193988595142}{253002341}e^{13} - \frac{131943952283}{253002341}e^{12} + \frac{858709023648}{253002341}e^{11} + \frac{895722571872}{253002341}e^{10} - \frac{2012656411103}{253002341}e^{9} - \frac{2530889694640}{253002341}e^{8} + \frac{2415061577875}{253002341}e^{7} + \frac{3384116148058}{253002341}e^{6} - \frac{1359235568529}{253002341}e^{5} - \frac{2054711018104}{253002341}e^{4} + \frac{272361317494}{253002341}e^{3} + \frac{444891884775}{253002341}e^{2} - \frac{1125178641}{253002341}e - \frac{2091979460}{253002341}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ | $1$ |