Properties

Label 4.4.17609.1-17.1-b
Base field 4.4.17609.1
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, w^{3} + w^{2} - 6w - 1]$
Dimension $32$
CM no
Base change no

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Base field 4.4.17609.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[17, 17, w^{3} + w^{2} - 6w - 1]$
Dimension: $32$
CM: no
Base change: no
Newspace dimension: $46$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{32} - 56x^{30} + 1418x^{28} - 21470x^{26} + 216604x^{24} - 1535949x^{22} + 7870771x^{20} - 29519143x^{18} + 81199114x^{16} - 162714149x^{14} + 233844048x^{12} - 234708210x^{10} + 157631077x^{8} - 65911521x^{6} + 14980930x^{4} - 1351666x^{2} + 18225\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $-\frac{1175440975143881}{1535782255792748912}e^{30} + \frac{60827825178435153}{1535782255792748912}e^{28} - \frac{1414153994362879027}{1535782255792748912}e^{26} + \frac{1501249198592959381}{118137096599442224}e^{24} - \frac{177965591036254768453}{1535782255792748912}e^{22} + \frac{564716090198906529969}{767891127896374456}e^{20} - \frac{5117970980049681247205}{1535782255792748912}e^{18} + \frac{321524218685421775047}{29534274149860556}e^{16} - \frac{19637552152724052232327}{767891127896374456}e^{14} + \frac{65431617388976137727139}{1535782255792748912}e^{12} - \frac{75276197307279146222051}{1535782255792748912}e^{10} + \frac{57234776268428553969165}{1535782255792748912}e^{8} - \frac{13386592208944613534409}{767891127896374456}e^{6} + \frac{6789447388356636156259}{1535782255792748912}e^{4} - \frac{708217478609220252349}{1535782255792748912}e^{2} + \frac{11263286537586402999}{1535782255792748912}$
7 $[7, 7, -w^{3} + 6w - 2]$ $-\frac{283712432628723089}{207330604532021103120}e^{31} + \frac{15621601709021503969}{207330604532021103120}e^{29} - \frac{387444703145648983027}{207330604532021103120}e^{27} + \frac{87973041032034399665}{3189701608184940048}e^{25} - \frac{55886101360178869214141}{207330604532021103120}e^{23} + \frac{7052041392177410084099}{3839455639481872280}e^{21} - \frac{1855123997297565318835469}{207330604532021103120}e^{19} + \frac{125355106016060967678731}{3987127010231175060}e^{17} - \frac{8231135746400779211538583}{103665302266010551560}e^{15} + \frac{29428704001243271786998531}{207330604532021103120}e^{13} - \frac{4019261184396711990145963}{23036733836891233680}e^{11} + \frac{647026445002090676787113}{4607346767378246736}e^{9} - \frac{7052185591470756701800369}{103665302266010551560}e^{7} + \frac{1159424666698792778522633}{69110201510673701040}e^{5} - \frac{54436732421577357914161}{41466120906404220624}e^{3} - \frac{3846076255019335999801}{207330604532021103120}e$
8 $[8, 2, w^{3} - 7w + 3]$ $-\frac{80495857349487809}{69110201510673701040}e^{31} + \frac{4388456030944395229}{69110201510673701040}e^{29} - \frac{107836187645990291107}{69110201510673701040}e^{27} + \frac{24282469408086167285}{1063233869394980016}e^{25} - \frac{15319295924461415980181}{69110201510673701040}e^{23} + \frac{5770385143309590032687}{3839455639481872280}e^{21} - \frac{504812913003307602219689}{69110201510673701040}e^{19} + \frac{34155358912712307428711}{1329042336743725020}e^{17} - \frac{2256664256832805415779843}{34555100755336850520}e^{15} + \frac{8173010006145125527934971}{69110201510673701040}e^{13} - \frac{1141421795004370542498423}{7678911278963744560}e^{11} + \frac{190555811445991501365905}{1535782255792748912}e^{9} - \frac{2207065014190413008493799}{34555100755336850520}e^{7} + \frac{408270109199866522203293}{23036733836891233680}e^{5} - \frac{27594662087810825506489}{13822040302134740208}e^{3} + \frac{4084578842292465442739}{69110201510673701040}e$
11 $[11, 11, -w^{3} + 6w - 4]$ $-\frac{29914547680876865}{27644080604269480416}e^{31} + \frac{1686428944518245113}{27644080604269480416}e^{29} - \frac{42784242864703114291}{27644080604269480416}e^{27} + \frac{49637801632222689925}{2126467738789960032}e^{25} - \frac{6438946337174640343757}{27644080604269480416}e^{23} + \frac{2486587727372259329493}{1535782255792748912}e^{21} - \frac{222290491178058375487469}{27644080604269480416}e^{19} + \frac{15309466703942777166137}{531616934697490008}e^{17} - \frac{1025075574963148397885743}{13822040302134740208}e^{15} + \frac{3744277368780932093953507}{27644080604269480416}e^{13} - \frac{524919701481612658691339}{3071564511585497824}e^{11} + \frac{438371810311097040370621}{3071564511585497824}e^{9} - \frac{1016658648743905808850373}{13822040302134740208}e^{7} + \frac{190482409986188763777881}{9214693534756493472}e^{5} - \frac{68134623746507490884525}{27644080604269480416}e^{3} + \frac{2112365710251547516031}{27644080604269480416}e$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $-1$
17 $[17, 17, -w^{2} - w + 3]$ $-\frac{168065117393892547}{69110201510673701040}e^{31} + \frac{9320687053160824547}{69110201510673701040}e^{29} - \frac{232935022694271629441}{69110201510673701040}e^{27} + \frac{53318392751455885819}{1063233869394980016}e^{25} - \frac{34163803821912999959263}{69110201510673701040}e^{23} + \frac{13053251948947651518591}{3839455639481872280}e^{21} - \frac{1156231274624734773567127}{69110201510673701040}e^{19} + \frac{79014264099844930185793}{1329042336743725020}e^{17} - \frac{5255745294480011455089569}{34555100755336850520}e^{15} + \frac{19082682988167595067405393}{69110201510673701040}e^{13} - \frac{2657257474407886109256569}{7678911278963744560}e^{11} + \frac{439136767286577735135507}{1535782255792748912}e^{9} - \frac{4979574885638403638210567}{34555100755336850520}e^{7} + \frac{880395145866068032345099}{23036733836891233680}e^{5} - \frac{51413623866504203095955}{13822040302134740208}e^{3} + \frac{1707966300414842587597}{69110201510673701040}e$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $\phantom{-}\frac{99875714335640419}{51832651133005275780}e^{31} - \frac{5446229841832263389}{51832651133005275780}e^{29} + \frac{133832477034416369927}{51832651133005275780}e^{27} - \frac{30125926578578545477}{797425402046235012}e^{25} + \frac{18987668166125745609691}{51832651133005275780}e^{23} - \frac{2379577119405354412319}{959863909870468070}e^{21} + \frac{622512196145540236062499}{51832651133005275780}e^{19} - \frac{41904051811723423384411}{996781752557793765}e^{17} + \frac{2747267912327983333136483}{25916325566502637890}e^{15} - \frac{9836985333620185457712071}{51832651133005275780}e^{13} + \frac{1351126183822621352985983}{5759183459222808420}e^{11} - \frac{220033272919676191193035}{1151836691844561684}e^{9} + \frac{2447379399376273149362099}{25916325566502637890}e^{7} - \frac{416621867676011183412043}{17277550377668425260}e^{5} + \frac{21220291598417690101103}{10366530226601055156}e^{3} + \frac{512414776022363446901}{51832651133005275780}e$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $\phantom{-}\frac{370982420043052891}{207330604532021103120}e^{31} - \frac{19694415657399913691}{207330604532021103120}e^{29} + \frac{470681511200050586393}{207330604532021103120}e^{27} - \frac{102965403976517752867}{3189701608184940048}e^{25} + \frac{63039436443968758285639}{207330604532021103120}e^{23} - \frac{7673867136264918721341}{3839455639481872280}e^{21} + \frac{1950942113163219295119631}{207330604532021103120}e^{19} - \frac{127763343987869306410969}{3987127010231175060}e^{17} + \frac{8163171331901607521518457}{103665302266010551560}e^{15} - \frac{28552295406435908688302729}{207330604532021103120}e^{13} + \frac{3841473640665515316752657}{23036733836891233680}e^{11} - \frac{614713504951029445817515}{4607346767378246736}e^{9} + \frac{6749430081329990283182111}{103665302266010551560}e^{7} - \frac{1149052290089487326399347}{69110201510673701040}e^{5} + \frac{62438992495390944964235}{41466120906404220624}e^{3} - \frac{291345888835307668981}{207330604532021103120}e$
41 $[41, 41, w^{2} + 2w - 4]$ $\phantom{-}\frac{5592586034376673}{69110201510673701040}e^{31} - \frac{370428077131870793}{69110201510673701040}e^{29} + \frac{10660562888889492179}{69110201510673701040}e^{27} - \frac{2736159955686652873}{1063233869394980016}e^{25} + \frac{1925717834338665620317}{69110201510673701040}e^{23} - \frac{794719017165459063029}{3839455639481872280}e^{21} + \frac{74945270265754424289973}{69110201510673701040}e^{19} - \frac{5380824223659131066527}{1329042336743725020}e^{17} + \frac{370980939681834828047831}{34555100755336850520}e^{15} - \frac{1373773519170880203955187}{69110201510673701040}e^{13} + \frac{190429711670167750657891}{7678911278963744560}e^{11} - \frac{29854584738567485801865}{1535782255792748912}e^{9} + \frac{280969601565774700444013}{34555100755336850520}e^{7} - \frac{19413896954531298237121}{23036733836891233680}e^{5} - \frac{5488423203635869579471}{13822040302134740208}e^{3} + \frac{3094108462679807878337}{69110201510673701040}e$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $-\frac{7889518404672287}{3071564511585497824}e^{30} + \frac{416184489519122887}{3071564511585497824}e^{28} - \frac{9895366389187294701}{3071564511585497824}e^{26} + \frac{10782401213170566939}{236274193198884448}e^{24} - \frac{1317249117545781224195}{3071564511585497824}e^{22} + \frac{4326611150443885008931}{1535782255792748912}e^{20} - \frac{40785647574542419035411}{3071564511585497824}e^{18} + \frac{2679381514198423351467}{59068548299721112}e^{16} - \frac{172142946475245399462953}{1535782255792748912}e^{14} + \frac{607331642752445762944509}{3071564511585497824}e^{12} - \frac{745121183595418121826013}{3071564511585497824}e^{10} + \frac{608237278138014882537355}{3071564511585497824}e^{8} - \frac{153087653639843652420283}{1535782255792748912}e^{6} + \frac{82226527523557289132757}{3071564511585497824}e^{4} - \frac{8318723340891368787299}{3071564511585497824}e^{2} + \frac{99549650767575423057}{3071564511585497824}$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $-\frac{123465821884762733}{34555100755336850520}e^{31} + \frac{6884855752613979733}{34555100755336850520}e^{29} - \frac{172980729659936753419}{34555100755336850520}e^{27} + \frac{39801376629580479401}{531616934697490008}e^{25} - \frac{25632789549476630833457}{34555100755336850520}e^{23} + \frac{9842864119122957957539}{1919727819740936140}e^{21} - \frac{876207686204429702661113}{34555100755336850520}e^{19} + \frac{30089775478270377529291}{332260584185931255}e^{17} - \frac{4023838781961635020817071}{17277550377668425260}e^{15} + \frac{14692842841035299322742507}{34555100755336850520}e^{13} - \frac{2059733669653768787911971}{3839455639481872280}e^{11} + \frac{343540270738424197366229}{767891127896374456}e^{9} - \frac{3958364432268564297779803}{17277550377668425260}e^{7} + \frac{726824142703510243442741}{11518366918445616840}e^{5} - \frac{48703031863491514311697}{6911020151067370104}e^{3} + \frac{6204867457159001710403}{34555100755336850520}e$
59 $[59, 59, -2w^{3} + 13w - 6]$ $\phantom{-}\frac{88569059511397529}{27644080604269480416}e^{31} - \frac{4788273195978859777}{27644080604269480416}e^{29} + \frac{116707947489788978395}{27644080604269480416}e^{27} - \frac{130376407041510739981}{2126467738789960032}e^{25} + \frac{16327545982015741485365}{27644080604269480416}e^{23} - \frac{6106342735760501774837}{1535782255792748912}e^{21} + \frac{530557466398640701859765}{27644080604269480416}e^{19} - \frac{35658753885135225621749}{531616934697490008}e^{17} + \frac{2340147696342221259788335}{13822040302134740208}e^{15} - \frac{8412921579978866025084715}{27644080604269480416}e^{13} + \frac{1164116822707738639253603}{3071564511585497824}e^{11} - \frac{958343519475108110224709}{3071564511585497824}e^{9} + \frac{2163406787090733096101413}{13822040302134740208}e^{7} - \frac{376230678442245054094721}{9214693534756493472}e^{5} + \frac{102635440430104485672629}{27644080604269480416}e^{3} - \frac{917205979680552324359}{27644080604269480416}e$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $\phantom{-}\frac{635097228557443}{191972781974093614}e^{30} - \frac{33967929165310215}{191972781974093614}e^{28} + \frac{818755813649868639}{191972781974093614}e^{26} - \frac{904093083023838491}{14767137074930278}e^{24} + \frac{111849525102115861329}{191972781974093614}e^{22} - \frac{371610094854777490631}{95986390987046807}e^{20} + \frac{3537282994049024994753}{191972781974093614}e^{18} - \frac{468107925655582815804}{7383568537465139}e^{16} + \frac{15089983798934508014924}{95986390987046807}e^{14} - \frac{53141522419122528037847}{191972781974093614}e^{12} + \frac{64582928208664077567365}{191972781974093614}e^{10} - \frac{51649655299243642142101}{191972781974093614}e^{8} + \frac{12537247128554772142279}{95986390987046807}e^{6} - \frac{6349961465194759920379}{191972781974093614}e^{4} + \frac{584254873710502465127}{191972781974093614}e^{2} - \frac{5761790338184681127}{191972781974093614}$
59 $[59, 59, w^{2} + w - 1]$ $-\frac{3014051199256723}{1772056448991633360}e^{31} + \frac{165916486487165363}{1772056448991633360}e^{29} - \frac{4114772438886590369}{1772056448991633360}e^{27} + \frac{12147852966160096927}{354411289798326672}e^{25} - \frac{593892241438650305287}{1772056448991633360}e^{23} + \frac{675042602705927102637}{295342741498605560}e^{21} - \frac{19758990519771425367943}{1772056448991633360}e^{19} + \frac{17396774602334873999791}{443014112247908340}e^{17} - \frac{88190569204023382680941}{886028224495816680}e^{15} + \frac{317157225546667033367777}{1772056448991633360}e^{13} - \frac{131206268265624707145883}{590685482997211120}e^{11} + \frac{21471910277155978437585}{118137096599442224}e^{9} - \frac{80378460612792837584183}{886028224495816680}e^{7} + \frac{14075625055454961812411}{590685482997211120}e^{5} - \frac{814995397770946942523}{354411289798326672}e^{3} + \frac{25374768606801331573}{1772056448991633360}e$
59 $[59, 59, w^{2} + 2w - 6]$ $-\frac{5157897373566981}{1535782255792748912}e^{30} + \frac{288791523286055277}{1535782255792748912}e^{28} - \frac{7282273369202525159}{1535782255792748912}e^{26} + \frac{8404465060762545209}{118137096599442224}e^{24} - \frac{1085362727157919315929}{1535782255792748912}e^{22} + \frac{3758434353505011184141}{767891127896374456}e^{20} - \frac{37221240859797801030793}{1535782255792748912}e^{18} + \frac{2557301080575028300231}{29534274149860556}e^{16} - \frac{170856736364111005821631}{767891127896374456}e^{14} + \frac{622454487249420130596951}{1535782255792748912}e^{12} - \frac{781838008489916663735327}{1535782255792748912}e^{10} + \frac{646630262018942670167313}{1535782255792748912}e^{8} - \frac{162810227291866235532205}{767891127896374456}e^{6} + \frac{86030630112551891199487}{1535782255792748912}e^{4} - \frac{8343856478735350064233}{1535782255792748912}e^{2} + \frac{117765527159467402323}{1535782255792748912}$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $-\frac{280573724049743123}{82932241812808441248}e^{31} + \frac{15615642094625739499}{82932241812808441248}e^{29} - \frac{391786637566988509177}{82932241812808441248}e^{27} + \frac{450343469310244297615}{6379403216369880096}e^{25} - \frac{57989926398242285759015}{82932241812808441248}e^{23} + \frac{7425482654076330858165}{1535782255792748912}e^{21} - \frac{1985325797343964134134807}{82932241812808441248}e^{19} + \frac{136639311204085375131863}{1594850804092470024}e^{17} - \frac{9165834310386650026450933}{41466120906404220624}e^{15} + \frac{33626449494597351111579721}{82932241812808441248}e^{13} - \frac{4744851323442366991535809}{9214693534756493472}e^{11} + \frac{3990885044096958163753399}{9214693534756493472}e^{9} - \frac{9287915716296325242160159}{41466120906404220624}e^{7} + \frac{1717623334665409837608347}{27644080604269480416}e^{5} - \frac{567771188971954886852807}{82932241812808441248}e^{3} + \frac{13105498955795025787565}{82932241812808441248}e$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $-\frac{92515157588403}{767891127896374456}e^{30} + \frac{15178737531032407}{767891127896374456}e^{28} - \frac{622316378059488357}{767891127896374456}e^{26} + \frac{979273503728312163}{59068548299721112}e^{24} - \frac{158074225190001977355}{767891127896374456}e^{22} + \frac{649164475812367166451}{383945563948187228}e^{20} - \frac{7356641852318749875167}{767891127896374456}e^{18} + \frac{281674661207267744183}{7383568537465139}e^{16} - \frac{41093962810600968028311}{383945563948187228}e^{14} + \frac{160702739226893206501701}{767891127896374456}e^{12} - \frac{213529239082076158910221}{767891127896374456}e^{10} + \frac{184413413175424040985355}{767891127896374456}e^{8} - \frac{47935241326685316990907}{383945563948187228}e^{6} + \frac{25935264173045570606473}{767891127896374456}e^{4} - \frac{2584834360284593430547}{767891127896374456}e^{2} + \frac{39861304824970297829}{767891127896374456}$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $\phantom{-}\frac{51975299577757187}{41466120906404220624}e^{31} - \frac{3045709526742487723}{41466120906404220624}e^{29} + \frac{80000270162594399809}{41466120906404220624}e^{27} - \frac{95741391666919905655}{3189701608184940048}e^{25} + \frac{12765422134022401842671}{41466120906404220624}e^{23} - \frac{1682998353952668437257}{767891127896374456}e^{21} + \frac{460516720862948293212455}{41466120906404220624}e^{19} - \frac{32217028092764448228047}{797425402046235012}e^{17} + \frac{2178785911188648950668321}{20733060453202110312}e^{15} - \frac{7972943512371684168333265}{41466120906404220624}e^{13} + \frac{1105197687646793708787433}{4607346767378246736}e^{11} - \frac{891193934691208636385311}{4607346767378246736}e^{9} + \frac{1898687178022721546721835}{20733060453202110312}e^{7} - \frac{285817970555647531081883}{13822040302134740208}e^{5} + \frac{40271306795186327507831}{41466120906404220624}e^{3} + \frac{3247872910504570135195}{41466120906404220624}e$
81 $[81, 3, -3]$ $-\frac{269382665507513}{118137096599442224}e^{30} + \frac{13580318431476305}{118137096599442224}e^{28} - \frac{306698726785377347}{118137096599442224}e^{26} + \frac{4099228209171918745}{118137096599442224}e^{24} - \frac{36089677502113038733}{118137096599442224}e^{22} + \frac{110241536172640113977}{59068548299721112}e^{20} - \frac{959590072480585067837}{118137096599442224}e^{18} + \frac{752031285407017430523}{29534274149860556}e^{16} - \frac{3396237670162121684395}{59068548299721112}e^{14} + \frac{10941202283804512478979}{118137096599442224}e^{12} - \frac{12311393464372963137819}{118137096599442224}e^{10} + \frac{9319836032006044707365}{118137096599442224}e^{8} - \frac{2218169812867954561833}{59068548299721112}e^{6} + \frac{1166971671471324657643}{118137096599442224}e^{4} - \frac{128448744458754339629}{118137096599442224}e^{2} + \frac{3234720865532803535}{118137096599442224}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, w^{3} + w^{2} - 6w - 1]$ $1$