Properties

Label 1.106.a
Level 1
Weight 106
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 106 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{106}(\Gamma_0(1))\).

Total New Old
Modular forms 9 9 0
Cusp forms 8 8 0
Eisenstein series 1 1 0

Trace form

\(8q \) \(\mathstrut -\mathstrut 9175032489175920q^{2} \) \(\mathstrut -\mathstrut 3552367551392844422995680q^{3} \) \(\mathstrut +\mathstrut 120400994563419904822151366840576q^{4} \) \(\mathstrut +\mathstrut 748366724871512021371292499759044400q^{5} \) \(\mathstrut -\mathstrut 132475226406122000574502252920799787081664q^{6} \) \(\mathstrut +\mathstrut 70538552172860257833295679508195640805531200q^{7} \) \(\mathstrut -\mathstrut 706397877636490430592988742663067828802762076160q^{8} \) \(\mathstrut +\mathstrut 317686049104616976165951103806454636773011694234984q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 9175032489175920q^{2} \) \(\mathstrut -\mathstrut 3552367551392844422995680q^{3} \) \(\mathstrut +\mathstrut 120400994563419904822151366840576q^{4} \) \(\mathstrut +\mathstrut 748366724871512021371292499759044400q^{5} \) \(\mathstrut -\mathstrut 132475226406122000574502252920799787081664q^{6} \) \(\mathstrut +\mathstrut 70538552172860257833295679508195640805531200q^{7} \) \(\mathstrut -\mathstrut 706397877636490430592988742663067828802762076160q^{8} \) \(\mathstrut +\mathstrut 317686049104616976165951103806454636773011694234984q^{9} \) \(\mathstrut +\mathstrut 44171640525838765855893406263279104758565541661288800q^{10} \) \(\mathstrut -\mathstrut 9131055394382837373664474069991492435117703171343284384q^{11} \) \(\mathstrut +\mathstrut 1527166610615675905236013736606832949994468355519571829760q^{12} \) \(\mathstrut +\mathstrut 4027585984285071020829060873004471073659148035689891664240q^{13} \) \(\mathstrut -\mathstrut 160479473931693657661766690342904266858167662972048261318528q^{14} \) \(\mathstrut -\mathstrut 85128562811603808162187988771451472214709069164574920929377600q^{15} \) \(\mathstrut +\mathstrut 889182208997906282405898151302671436269823882827077347193192448q^{16} \) \(\mathstrut -\mathstrut 47501502884916058924984340290257937633075778259367096814503394160q^{17} \) \(\mathstrut -\mathstrut 2631080775730316510475478098580289149623650642713560969940755311280q^{18} \) \(\mathstrut -\mathstrut 18490664070300440944092597449321411045310230817014503422448283738720q^{19} \) \(\mathstrut -\mathstrut 433265654737251440411002845299403120817887965583462605623471811443200q^{20} \) \(\mathstrut +\mathstrut 3435707407505559395644737215619994347818097875706879454950102719283456q^{21} \) \(\mathstrut +\mathstrut 61667954680464912832813918015747124830645650785532527356368764542445760q^{22} \) \(\mathstrut +\mathstrut 356123479312529060531796005710488420903589988587191444144805952706144960q^{23} \) \(\mathstrut -\mathstrut 8553895157762497374674387748794258238227739674467572965053160752231464960q^{24} \) \(\mathstrut +\mathstrut 36710330225103772037154153143396858524815591923552301173280524244928235000q^{25} \) \(\mathstrut -\mathstrut 178290299429521612994896681862440451353112938442078389560127528645835464224q^{26} \) \(\mathstrut +\mathstrut 4108583825736723245642984497148380325909672596193180989676962467681728811840q^{27} \) \(\mathstrut -\mathstrut 10197863837452248524370326511788692919181508212113555118341665631868445276160q^{28} \) \(\mathstrut -\mathstrut 132808057928545728770070628075237950532883381334274325807559945373631525579280q^{29} \) \(\mathstrut +\mathstrut 368843646251862307061952875207762300737776646306173378951277228159200294844800q^{30} \) \(\mathstrut +\mathstrut 2123150329739540390115408696476884203950374929670685127189943125782378108098816q^{31} \) \(\mathstrut +\mathstrut 10156626912480412308164375397145246760285661187761787998479811379273048947425280q^{32} \) \(\mathstrut -\mathstrut 110453822927144134530855124481163271865404195805770611489444997754143335676114560q^{33} \) \(\mathstrut +\mathstrut 626514570831444006665132709400608888132203790316575476126972954148191421104888352q^{34} \) \(\mathstrut -\mathstrut 180124138596474130911007456858429985683613480525844149859433273467968580724675200q^{35} \) \(\mathstrut +\mathstrut 16221855297378912428170473077312544781163834427405933513071046969489436648368930048q^{36} \) \(\mathstrut -\mathstrut 23010049861253897057830375004531412092720779537210279421336409908255568411112521680q^{37} \) \(\mathstrut +\mathstrut 81514285558726303526499020366236482021009949677570093462995405282915730851685437760q^{38} \) \(\mathstrut +\mathstrut 973250204883059182004683876455057324018758755152662643519744443013209490499392320448q^{39} \) \(\mathstrut +\mathstrut 1620603767802466493396978076732241543088378147649587002013209944275991354096540672000q^{40} \) \(\mathstrut -\mathstrut 9194436894335705500488956082645864740213392167963146808356372625255538188465570116784q^{41} \) \(\mathstrut -\mathstrut 9987175533659763810738086904398668829743024019181589555089340923029980612539996188160q^{42} \) \(\mathstrut +\mathstrut 3032382926300215248368351846801184405080019611637638159804034319071519733367501308000q^{43} \) \(\mathstrut -\mathstrut 61413740744912033848381562467905778729130346597543024132573739224535613780500625691648q^{44} \) \(\mathstrut -\mathstrut 728055588424370630925028219171725592820104067843765840180299922436159334808200708678800q^{45} \) \(\mathstrut -\mathstrut 1937857727868547524263658836001472070613971220638572213222135000017628068861666423993984q^{46} \) \(\mathstrut -\mathstrut 193114845358989650895015242618332478679741488577861492750207342621672434970683481651840q^{47} \) \(\mathstrut +\mathstrut 47504655695285299018807413925656103836145592812920588522461073427843872384146136331714560q^{48} \) \(\mathstrut +\mathstrut 9009795911083753626429293565600536034814214101588418291494061693709008119369143800410056q^{49} \) \(\mathstrut +\mathstrut 124085104852024153585775552318382585485956095474767588057564984609967735836202360766470000q^{50} \) \(\mathstrut -\mathstrut 1021523462097644786402134875264470962590383726411120471709206304906745531337979847222893504q^{51} \) \(\mathstrut +\mathstrut 2601002607846544407071841678151669268750253239046498757166255249010956826575867860287884800q^{52} \) \(\mathstrut -\mathstrut 508977518161307968273832984082037167871777334860039281483640147609506187672311865310329680q^{53} \) \(\mathstrut -\mathstrut 33215015372693850873232010101241869628048359784733721234902490207672455295016159119447797120q^{54} \) \(\mathstrut +\mathstrut 18450671784502163418133731529996697688391744925805957647904016734511230779675351655763828800q^{55} \) \(\mathstrut +\mathstrut 77907763278563265290300076439200648252399491244631034718538984366849741317596223703232839680q^{56} \) \(\mathstrut -\mathstrut 17514494370932414539251899866861034389141458703710767594438206182965846210727691039357326720q^{57} \) \(\mathstrut +\mathstrut 521188643454307966215167554048547429862263982605454645813054246139388891719965181350028489440q^{58} \) \(\mathstrut -\mathstrut 800548783090069547249411402735852579353665443321854402294237928007339127684491029048409334560q^{59} \) \(\mathstrut -\mathstrut 4945597330350911740055109354650466378405725800344464689989883069207313581778154248500120627200q^{60} \) \(\mathstrut +\mathstrut 9301780115240647873952088718367909265400456376594614456607735293030740558435392467259218034416q^{61} \) \(\mathstrut -\mathstrut 24958988483741760731654226022541604930667635314913646027823754011402485431605464535556971159040q^{62} \) \(\mathstrut -\mathstrut 69917019353683231050173137254943101675489279093995056831426882673091272292662113138105940233920q^{63} \) \(\mathstrut -\mathstrut 97451971150817117830440198299734679886485437857461550467094176739811166528413095345956746952704q^{64} \) \(\mathstrut -\mathstrut 361156613980852842706992602837566394553099687955520933659145529501075901774183231590989074101600q^{65} \) \(\mathstrut +\mathstrut 156882494260210220362013449528635783983344936752786747375982538482579620426751742603199124015872q^{66} \) \(\mathstrut -\mathstrut 1104667221349188765660578837514456152306124133482553297212406551469220909847432127137057601268960q^{67} \) \(\mathstrut -\mathstrut 9721401068443204036258202986739714019478462517573215331908850090837288931485135338678529805012480q^{68} \) \(\mathstrut -\mathstrut 15109507425538340400955372418178718530943009113130778845692031950392404855615907056642892252773632q^{69} \) \(\mathstrut -\mathstrut 42141974870106016058865849455224368290398026088671930674752184932090288769297201065857297686150400q^{70} \) \(\mathstrut -\mathstrut 50469870302247936824042683436030531088994086024328522294948330069784198912349909975813351349301184q^{71} \) \(\mathstrut -\mathstrut 312770283013563627062551283668577288708985871414226238388562703871210081634250694390516261706772480q^{72} \) \(\mathstrut -\mathstrut 309796921364548112330210024475355394269902333254274320239737341959226533985104691513778940551838640q^{73} \) \(\mathstrut -\mathstrut 925823752396046652342642416972554390081562347656534041993730400149451972597268102227614960148886688q^{74} \) \(\mathstrut -\mathstrut 2035970471601402025465859080535649095398414802703074791592862122373110362938204069403415245277940000q^{75} \) \(\mathstrut -\mathstrut 3130569503520776632201267436445813580876068550759173850078744887758531600111432515821247207535037440q^{76} \) \(\mathstrut -\mathstrut 5943612343311427733153258808379776193285399172298997030946865449540200274638852351419681744544800000q^{77} \) \(\mathstrut -\mathstrut 21269159569550168394975895479661937627684008715929340977029750772463946126724250407354989139174454400q^{78} \) \(\mathstrut -\mathstrut 15393227887174294584948162208020437185460179522932597986148734991937027143223423856935347902468612480q^{79} \) \(\mathstrut -\mathstrut 36135869014387530593279194332920203124385252019916366550807261806779025414796891084911471716850073600q^{80} \) \(\mathstrut -\mathstrut 16813579079052539310958564290225362908835005641306645336831720897045685008922728854885093229369750072q^{81} \) \(\mathstrut +\mathstrut 40683812685771158034068852888314888590966014976906157199478748314343833251276146968126649606561452960q^{82} \) \(\mathstrut -\mathstrut 27748711091393049888979586421607112972809560782068769478686312453860122910561653683460280801656090720q^{83} \) \(\mathstrut +\mathstrut 243729273671324707074190479881332236879714714008146405350632616637128634259974190017728217778172076032q^{84} \) \(\mathstrut +\mathstrut 1114476595266646322768819965977266122931255323002065012571315493969146685766458335643036439956923496800q^{85} \) \(\mathstrut +\mathstrut 2001948212296635436448279509615999770689923972184784294781573198292641086063207267886445869810840226496q^{86} \) \(\mathstrut +\mathstrut 2452094134677213482937709450778797624299131398431787829024781103485568458306913143764742103712037328320q^{87} \) \(\mathstrut +\mathstrut 6587629213482246089116430616322572992490320338289310595388533189153014205464262604258615522799278407680q^{88} \) \(\mathstrut +\mathstrut 4561891385239988132989403179389372513149936713239528905622804144400695279296267497385381892983137482960q^{89} \) \(\mathstrut +\mathstrut 27831127206069462137128463558919625443225864994138363209261172284208865542079088020097519776839212242400q^{90} \) \(\mathstrut +\mathstrut 27533535014530695422075480606590604897330716562374502844003945844898533709216751249129046131797307879296q^{91} \) \(\mathstrut +\mathstrut 11219382355167481799152672023779859908676464262842813795936572357113636635896010169112116501983056189440q^{92} \) \(\mathstrut -\mathstrut 1816432822902220399473532579920329564793343562884883929779919263741160765335835765675399623257440680960q^{93} \) \(\mathstrut -\mathstrut 145721137880009419474465571784854076810270560388958588104991210830700849472154051473896292058236218084608q^{94} \) \(\mathstrut -\mathstrut 197505250338784881028096044265210353994741936910104745900078290549992685412473006655125953841487400936000q^{95} \) \(\mathstrut -\mathstrut 722643410665348223758010527434181844660741784808619153000544243764286894029121981921039078126765698187264q^{96} \) \(\mathstrut -\mathstrut 765925425726897926053834041674103560846690860133522436616120766353705349104461208876007591285452102784240q^{97} \) \(\mathstrut -\mathstrut 1378222404256086778845054197358441766991528993251977664562346500406878280455090891540290251693972016377840q^{98} \) \(\mathstrut -\mathstrut 2543675383725234370604494641035024609729543664951752733885226452347175058619125118596469912791508615603232q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{106}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.106.a.a \(8\) \(69.819\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-9\!\cdots\!20\) \(-3\!\cdots\!80\) \(74\!\cdots\!00\) \(70\!\cdots\!00\) \(+\) \(q+(-1146879061146990+\beta _{1})q^{2}+\cdots\)