Base field \(\Q(\sqrt{401}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 100\); narrow class number \(5\) and class number \(5\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $32$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $135$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{32} - 2x^{31} + 22x^{30} - 50x^{29} + 352x^{28} - 496x^{27} + 4236x^{26} - 5011x^{25} + 47974x^{24} - 55716x^{23} + 385112x^{22} - 364068x^{21} + 2643937x^{20} - 673414x^{19} + 13357861x^{18} - 6418932x^{17} + 62958930x^{16} - 57214233x^{15} + 96390362x^{14} - 79478282x^{13} + 107514231x^{12} - 67236041x^{11} + 85013251x^{10} - 54218016x^{9} + 65122843x^{8} - 43728276x^{7} + 33507701x^{6} - 16743222x^{5} + 11698249x^{4} - 2613828x^{3} + 573840x^{2} - 115776x + 20736\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $...$ |
| 2 | $[2, 2, w + 1]$ | $...$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $...$ |
| 7 | $[7, 7, w + 1]$ | $...$ |
| 7 | $[7, 7, w + 5]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 7]$ | $...$ |
| 29 | $[29, 29, w + 6]$ | $...$ |
| 29 | $[29, 29, w + 22]$ | $...$ |
| 41 | $[41, 41, w + 13]$ | $...$ |
| 41 | $[41, 41, w + 27]$ | $...$ |
| 43 | $[43, 43, w + 16]$ | $...$ |
| 43 | $[43, 43, w + 26]$ | $...$ |
| 47 | $[47, 47, w + 2]$ | $...$ |
| 47 | $[47, 47, w + 44]$ | $...$ |
| 73 | $[73, 73, w + 33]$ | $...$ |
| 73 | $[73, 73, w + 39]$ | $...$ |
| 83 | $[83, 83, -4w - 37]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-\frac{23336019558716116845977591155030584725201}{2151116083286022618282141792976463888403355200}e^{31} + \frac{23381846511071059387016378273809104760529}{1075558041643011309141070896488231944201677600}e^{30} - \frac{256729817896990042226568933625928270850427}{1075558041643011309141070896488231944201677600}e^{29} + \frac{584269018826820403593889172841186093085289}{1075558041643011309141070896488231944201677600}e^{28} - \frac{256758579354104361129830840235281307828859}{67222377602688206821316931030514496512604850}e^{27} + \frac{145002691477237345439395660153248501828163}{26888951041075282728526772412205798605041940}e^{26} - \frac{8237919507977561186138978441312915539183153}{179259673607168551523511816081371990700279600}e^{25} + \frac{117254117182364445811666964976044152460589827}{2151116083286022618282141792976463888403355200}e^{24} - \frac{111948927673569787656611023330724059016426759}{215111608328602261828214179297646388840335520}e^{23} + \frac{108653263833906447857146510561631753312367763}{179259673607168551523511816081371990700279600}e^{22} - \frac{1123320043287998110695367417573856530904471291}{268889510410752827285267724122057986050419400}e^{21} + \frac{15782967645083806140866223250632870657245087}{3983548302381523367189151468474933126672880}e^{20} - \frac{61688164455780233380478812346405121047950179761}{2151116083286022618282141792976463888403355200}e^{19} + \frac{7950210542683312595998420589058427099546457011}{1075558041643011309141070896488231944201677600}e^{18} - \frac{311483087884554500592791522104357041998523651893}{2151116083286022618282141792976463888403355200}e^{17} + \frac{12569867594962634762602137223984008585469223599}{179259673607168551523511816081371990700279600}e^{16} - \frac{244732879041938498496342006948566808823475371859}{358519347214337103047023632162743981400559200}e^{15} + \frac{148844448436950889815254231784337370103915178273}{239012898142891402031349088108495987600372800}e^{14} - \frac{224793439753216721186395323462483371878904840857}{215111608328602261828214179297646388840335520}e^{13} + \frac{927135348003113768794768177251213869969575801109}{1075558041643011309141070896488231944201677600}e^{12} - \frac{835627253715430699033652099513973725763634000909}{717038694428674206094047264325487962801118400}e^{11} + \frac{1568537624819054658856955690283483719077707907609}{2151116083286022618282141792976463888403355200}e^{10} - \frac{1982694908120629405499332611279622838772193192691}{2151116083286022618282141792976463888403355200}e^{9} + \frac{4391652151125807375468708854323859083588087217}{7469153066965356313479659003390499612511650}e^{8} - \frac{303697983704253796487319326997883810155937179343}{430223216657204523656428358595292777680671040}e^{7} + \frac{84974532640610197251495134273504119158834295079}{179259673607168551523511816081371990700279600}e^{6} - \frac{31247642223738652763665636365546517328409243469}{86044643331440904731285671719058555536134208}e^{5} + \frac{21391092922285534765387529927441210296621156819}{119506449071445701015674544054247993800186400}e^{4} - \frac{272660104226508053115287760532863290340523743641}{2151116083286022618282141792976463888403355200}e^{3} + \frac{5076856817292318595554699800885843750409420491}{179259673607168551523511816081371990700279600}e^{2} - \frac{3715187987814325759653157075657778905671305}{597532245357228505078372720271239969000932}e + \frac{1561555844897675854427556129027795249365171}{1244858844494226052246609833898416602085275}$ |
| $2$ | $[2, 2, w + 1]$ | $-\frac{2607392967115697045858363852742162317}{2987661226786142525391863601356199845004660}e^{31} + \frac{7792103648052150196392280646648441024}{3734576533482678156739829501695249806255825}e^{30} - \frac{288673089836432001806970272081303963561}{14938306133930712626959318006780999225023300}e^{29} + \frac{187253990792253234407051994289770348358}{3734576533482678156739829501695249806255825}e^{28} - \frac{2332395774777110020504483130435065385887}{7469153066965356313479659003390499612511650}e^{27} + \frac{262738541845526685952349738579280196121}{497943537797690420898643933559366640834110}e^{26} - \frac{549221555568175773998837156203611210301}{149383061339307126269593180067809992250233}e^{25} + \frac{83409721239237736073353437776352509768171}{14938306133930712626959318006780999225023300}e^{24} - \frac{30838589454980893365537455582347348053281}{746915306696535631347965900339049961251165}e^{23} + \frac{187293316565351997602574411581158902208793}{2987661226786142525391863601356199845004660}e^{22} - \frac{819414900778334040488585887927904591429151}{2489717688988452104493219667796833204170550}e^{21} + \frac{527313325651960148832599347389248495070678}{1244858844494226052246609833898416602085275}e^{20} - \frac{11081759477744086369338402273153652493567291}{4979435377976904208986439335593666408341100}e^{19} + \frac{994281191608058423728625951828068554158552}{746915306696535631347965900339049961251165}e^{18} - \frac{39106606547480344706880914808875731754428208}{3734576533482678156739829501695249806255825}e^{17} + \frac{37663112932299917287483630594458471276006421}{3734576533482678156739829501695249806255825}e^{16} - \frac{149007057211115705731701569240439988650686417}{2987661226786142525391863601356199845004660}e^{15} + \frac{344817789077881774822509963215902998096025063}{4979435377976904208986439335593666408341100}e^{14} - \frac{522043269911126669441156388410323280942530027}{7469153066965356313479659003390499612511650}e^{13} + \frac{1153563104186989725964154483018432237121596957}{14938306133930712626959318006780999225023300}e^{12} - \frac{1142233575042822582172848111254906788181830529}{14938306133930712626959318006780999225023300}e^{11} + \frac{918189051828181572517968212596468124795602249}{14938306133930712626959318006780999225023300}e^{10} - \frac{345203431245069630809065630861750288791673013}{7469153066965356313479659003390499612511650}e^{9} + \frac{749653975623899048152879857534624178523887589}{14938306133930712626959318006780999225023300}e^{8} - \frac{132594987603053664706489055580190751296642817}{3734576533482678156739829501695249806255825}e^{7} + \frac{91974485662697146449516330161026145090865969}{2489717688988452104493219667796833204170550}e^{6} - \frac{6936990523362878682504842194833979561467107}{497943537797690420898643933559366640834110}e^{5} + \frac{2131724390261008487533477722018691941495127}{248971768898845210449321966779683320417055}e^{4} - \frac{2380764771165915739589200938031595168015916}{1244858844494226052246609833898416602085275}e^{3} + \frac{520514471715795646156553445266277522513456}{1244858844494226052246609833898416602085275}e^{2} + \frac{64909794562006526913661763970875810387097737}{14938306133930712626959318006780999225023300}e + \frac{17672491073782276645417692506598664242432}{1244858844494226052246609833898416602085275}$ |