Properties

Label 1.66.a
Level 1
Weight 66
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 66 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{66}(\Gamma_0(1))\).

Total New Old
Modular forms 6 6 0
Cusp forms 5 5 0
Eisenstein series 1 1 0

Trace form

\(5q \) \(\mathstrut -\mathstrut 3959709648q^{2} \) \(\mathstrut -\mathstrut 2231307434935404q^{3} \) \(\mathstrut +\mathstrut 116912191997379733760q^{4} \) \(\mathstrut +\mathstrut 26879673327548389029150q^{5} \) \(\mathstrut -\mathstrut 33295729280564090947602240q^{6} \) \(\mathstrut -\mathstrut 6923148241844308586296558808q^{7} \) \(\mathstrut -\mathstrut 446887903591926627901545861120q^{8} \) \(\mathstrut +\mathstrut 31912530537586467884680398342465q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 3959709648q^{2} \) \(\mathstrut -\mathstrut 2231307434935404q^{3} \) \(\mathstrut +\mathstrut 116912191997379733760q^{4} \) \(\mathstrut +\mathstrut 26879673327548389029150q^{5} \) \(\mathstrut -\mathstrut 33295729280564090947602240q^{6} \) \(\mathstrut -\mathstrut 6923148241844308586296558808q^{7} \) \(\mathstrut -\mathstrut 446887903591926627901545861120q^{8} \) \(\mathstrut +\mathstrut 31912530537586467884680398342465q^{9} \) \(\mathstrut -\mathstrut 46444835254758466872049375039200q^{10} \) \(\mathstrut -\mathstrut 5436990447821613455266185060489540q^{11} \) \(\mathstrut +\mathstrut 195800126486592722298045722544448512q^{12} \) \(\mathstrut -\mathstrut 2890859300726790832888435764458467514q^{13} \) \(\mathstrut +\mathstrut 41180574237900302034722115163160949120q^{14} \) \(\mathstrut +\mathstrut 103408365234403422747890968078751873400q^{15} \) \(\mathstrut -\mathstrut 1473868696955444538230489908858040811520q^{16} \) \(\mathstrut +\mathstrut 13864680686430637673540501618888491948122q^{17} \) \(\mathstrut -\mathstrut 52766923382337010938622933627608214498704q^{18} \) \(\mathstrut -\mathstrut 532140170263349448171574488831326440156700q^{19} \) \(\mathstrut +\mathstrut 3499008192062174379356405538388976603788800q^{20} \) \(\mathstrut -\mathstrut 11546436905526557006526119132251889169971040q^{21} \) \(\mathstrut +\mathstrut 22561892587607883403404755239099221639703104q^{22} \) \(\mathstrut -\mathstrut 94948785027142700354971234970110107282841224q^{23} \) \(\mathstrut -\mathstrut 2324009070474316353878252433966072715423334400q^{24} \) \(\mathstrut -\mathstrut 89368364701600219577770390611457383673793125q^{25} \) \(\mathstrut -\mathstrut 30521938596122123780659173092206061048452902240q^{26} \) \(\mathstrut -\mathstrut 129706546221561841046313530503436938966984152120q^{27} \) \(\mathstrut -\mathstrut 518698434811712968791028896222612623314185598976q^{28} \) \(\mathstrut -\mathstrut 1144597713377055966543673581436050616842314015850q^{29} \) \(\mathstrut -\mathstrut 8898165260141424207772350064014611180432376163200q^{30} \) \(\mathstrut -\mathstrut 4708831653623167525869999868687533742455793996640q^{31} \) \(\mathstrut -\mathstrut 23840662820937316611832895513659338085021120462848q^{32} \) \(\mathstrut -\mathstrut 47088400041590886495026610585051639514556983630608q^{33} \) \(\mathstrut +\mathstrut 65410975808473083189009824374957335825741658669920q^{34} \) \(\mathstrut +\mathstrut 431016017471985629901399384019473069677000966146800q^{35} \) \(\mathstrut +\mathstrut 1775126313486315490006860454334179833046020355380480q^{36} \) \(\mathstrut +\mathstrut 2530086119390649596783488597048185172700211081307582q^{37} \) \(\mathstrut +\mathstrut 8239199056511383470655384896825357549181759120989120q^{38} \) \(\mathstrut +\mathstrut 4961423111454378211563271585245526388719534092320280q^{39} \) \(\mathstrut -\mathstrut 40685898216651980081843388349290441658499772853248000q^{40} \) \(\mathstrut -\mathstrut 32007461843289961215814846894363640801437553437785390q^{41} \) \(\mathstrut -\mathstrut 195314045299892072857192155130437414288210017195751936q^{42} \) \(\mathstrut -\mathstrut 402059303617352898401840600044858362031212461462830244q^{43} \) \(\mathstrut -\mathstrut 612244818796766798372650999094717302459543241837614080q^{44} \) \(\mathstrut +\mathstrut 1043713954525992259035161696571453857355706435519522950q^{45} \) \(\mathstrut +\mathstrut 2514856669257653110995391415101692168449088734110815360q^{46} \) \(\mathstrut +\mathstrut 1572646433047878010336915637334684433480129688652944112q^{47} \) \(\mathstrut +\mathstrut 24675155031348794802454414815955354749687650397068722176q^{48} \) \(\mathstrut +\mathstrut 16734108893933327602070337185312116893972489911225126685q^{49} \) \(\mathstrut -\mathstrut 11063577880472461941859651947553302608752466885786430000q^{50} \) \(\mathstrut -\mathstrut 95495399267422751891095337933943462124412320320925036440q^{51} \) \(\mathstrut -\mathstrut 183526322178405888877826050411801068824199241263844049408q^{52} \) \(\mathstrut -\mathstrut 95621521245111298200083441902514245466096845017659053554q^{53} \) \(\mathstrut -\mathstrut 557318597848485774743582734276566483558675400940047747200q^{54} \) \(\mathstrut -\mathstrut 383625033771696018967747534079220095868070927508130274200q^{55} \) \(\mathstrut +\mathstrut 1279479797562181227760971870185499697207329786220906905600q^{56} \) \(\mathstrut +\mathstrut 3318990221727917572672253796992679057503071099524130319760q^{57} \) \(\mathstrut +\mathstrut 8032881606980455898794762567234097793264864123190024459680q^{58} \) \(\mathstrut -\mathstrut 2559150002019539763980782190342674875710406916414141257300q^{59} \) \(\mathstrut +\mathstrut 15929220555559091493107654286005818307326801014009906124800q^{60} \) \(\mathstrut +\mathstrut 3946890902136488204413925902971677716173875604816310291510q^{61} \) \(\mathstrut -\mathstrut 92928211608041968363364267171290588248132222513261182532096q^{62} \) \(\mathstrut -\mathstrut 68802271924921645132530256442236118351318471682753406875384q^{63} \) \(\mathstrut -\mathstrut 69150375570305937045593462943529104399703176808647979171840q^{64} \) \(\mathstrut -\mathstrut 203428189337486180767895923031910965130055608932610312683100q^{65} \) \(\mathstrut +\mathstrut 326824005648317890913619314213537102979279278284539154417920q^{66} \) \(\mathstrut +\mathstrut 479747394632655989552085275852886843492252096722130444354772q^{67} \) \(\mathstrut +\mathstrut 420712177041165958943716953506888102330291794585554871017984q^{68} \) \(\mathstrut +\mathstrut 2085757498496947569861287804370568246775481786853310358067680q^{69} \) \(\mathstrut +\mathstrut 2223344131713304350953089067854023542847735414462666460473600q^{70} \) \(\mathstrut -\mathstrut 3493409458155820303614582574535715900391996656268214500281240q^{71} \) \(\mathstrut -\mathstrut 6018736038355998608239490168867843174641985013841657017077760q^{72} \) \(\mathstrut +\mathstrut 733760875924726020894973106598755498748960690384116338055026q^{73} \) \(\mathstrut -\mathstrut 15514223525339201048939769580727994056556223964900985146362080q^{74} \) \(\mathstrut -\mathstrut 14732126168569891490987332632351786074968338319638722054452500q^{75} \) \(\mathstrut -\mathstrut 36133342560695069070126026304846041053110806476015652787276800q^{76} \) \(\mathstrut +\mathstrut 25871798846989842274158113588872654076768674584213145553762784q^{77} \) \(\mathstrut +\mathstrut 152853676099484832021645784710928259514016680275865958517430912q^{78} \) \(\mathstrut +\mathstrut 59699536569481886874118825694486111435856996884515844586586000q^{79} \) \(\mathstrut +\mathstrut 219177295509817100053456351931646916206927220422985017075302400q^{80} \) \(\mathstrut -\mathstrut 65583962416587044196237908629906173582326728520698989687871395q^{81} \) \(\mathstrut -\mathstrut 142296434381269688499177453649327032329978008843889237410699296q^{82} \) \(\mathstrut +\mathstrut 209047534837132969695050943022419892956201321886275074830990116q^{83} \) \(\mathstrut -\mathstrut 1354709036605046757778457263098823484206949849923331537372897280q^{84} \) \(\mathstrut -\mathstrut 1670550938011517784167531235760024383135110452768829071189193700q^{85} \) \(\mathstrut -\mathstrut 1010926193522040357819139524349238009908059943237053024421679040q^{86} \) \(\mathstrut -\mathstrut 13125541831432259160108322296931402049512991915132402846472360q^{87} \) \(\mathstrut +\mathstrut 3795986156893622389528985077855302896604937707291737426546933760q^{88} \) \(\mathstrut +\mathstrut 1493974679319648583095502764787645056501586744645243776851520450q^{89} \) \(\mathstrut +\mathstrut 11168691266815947461428091063256972957381716390895407392159178400q^{90} \) \(\mathstrut +\mathstrut 2617522707396973663766320817347076504527878438540996722544653360q^{91} \) \(\mathstrut +\mathstrut 5247747536363486457856850601737389388282095910031013129592297472q^{92} \) \(\mathstrut +\mathstrut 18739223210125935355706186663397055877109210120967221009013809792q^{93} \) \(\mathstrut -\mathstrut 12861091983377738108305257044091193029406256915207083515703514880q^{94} \) \(\mathstrut -\mathstrut 82117654407511305658368168133560153272734117033702557537140601000q^{95} \) \(\mathstrut -\mathstrut 56452805466036872845515504865736329476063459354106526340942397440q^{96} \) \(\mathstrut -\mathstrut 31085940707578182510537462951801111142341367310530261899829858838q^{97} \) \(\mathstrut -\mathstrut 46798198452208171360777266613142082443922483732249545388761625936q^{98} \) \(\mathstrut -\mathstrut 36017030678524367090996061767134771004855794650938085175529135220q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{66}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.66.a.a \(5\) \(26.757\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-3959709648\) \(-2\!\cdots\!04\) \(26\!\cdots\!50\) \(-6\!\cdots\!08\) \(+\) \(q+(-791941930-\beta _{1})q^{2}+(-446261486940055+\cdots)q^{3}+\cdots\)