Properties

Label 3.65.b
Level 3
Weight 65
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 20
Newforms 1
Sturm bound 21
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 65 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(21\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{65}(3, [\chi])\).

Total New Old
Modular forms 22 22 0
Cusp forms 20 20 0
Eisenstein series 2 2 0

Trace form

\(20q \) \(\mathstrut -\mathstrut 1420757969558292q^{3} \) \(\mathstrut -\mathstrut 157501780884986390320q^{4} \) \(\mathstrut -\mathstrut 7007663926080441102858480q^{6} \) \(\mathstrut +\mathstrut 682116984600047763945825976q^{7} \) \(\mathstrut -\mathstrut 2289432393664418080316877857100q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut -\mathstrut 1420757969558292q^{3} \) \(\mathstrut -\mathstrut 157501780884986390320q^{4} \) \(\mathstrut -\mathstrut 7007663926080441102858480q^{6} \) \(\mathstrut +\mathstrut 682116984600047763945825976q^{7} \) \(\mathstrut -\mathstrut 2289432393664418080316877857100q^{9} \) \(\mathstrut +\mathstrut 331029217205387677806996511116000q^{10} \) \(\mathstrut +\mathstrut 6534659062821156745233165595144848q^{12} \) \(\mathstrut -\mathstrut 751508903297384088692483175344422424q^{13} \) \(\mathstrut +\mathstrut 38547509823020584674418593740816815200q^{15} \) \(\mathstrut +\mathstrut 333898239622199115079798041399657464960q^{16} \) \(\mathstrut -\mathstrut 3676009515412490831675032229198156934240q^{18} \) \(\mathstrut +\mathstrut 109286088964872656413026262415428611794200q^{19} \) \(\mathstrut -\mathstrut 1311511276150890256934838463853331394769880q^{21} \) \(\mathstrut -\mathstrut 8079025213365934710514462143494926255299360q^{22} \) \(\mathstrut +\mathstrut 371409898348173331095205935880826344773509760q^{24} \) \(\mathstrut -\mathstrut 1408933246315215357541047632909406493714979500q^{25} \) \(\mathstrut +\mathstrut 5130931947084052629864823829892614277399503148q^{27} \) \(\mathstrut -\mathstrut 38556600155873290275414028639950032296787869664q^{28} \) \(\mathstrut -\mathstrut 141541842553229550692763020870574637255687216800q^{30} \) \(\mathstrut +\mathstrut 458034135616019870141982361360522347620359726840q^{31} \) \(\mathstrut -\mathstrut 2882270174679362228632701138961802589863549285280q^{33} \) \(\mathstrut -\mathstrut 787058086714062550476148644876342688312553235840q^{34} \) \(\mathstrut +\mathstrut 75759088962200911205216155020070755577873854233040q^{36} \) \(\mathstrut -\mathstrut 167241277488128791881901510734045117370850836062104q^{37} \) \(\mathstrut +\mathstrut 458879560232529079697344976545706436533594974010520q^{39} \) \(\mathstrut -\mathstrut 3172271879697225400792978571433360199916055661804800q^{40} \) \(\mathstrut -\mathstrut 22013931366996449796115743111552261520406610644630880q^{42} \) \(\mathstrut +\mathstrut 10353394041775726307362489381794503494462017586072216q^{43} \) \(\mathstrut +\mathstrut 37622210359250231761078599539977430954460378542462400q^{45} \) \(\mathstrut -\mathstrut 297398119355935548173345475928562088559055731847559360q^{46} \) \(\mathstrut -\mathstrut 127296049249148961420276393789708282996205874832565632q^{48} \) \(\mathstrut +\mathstrut 2035505279477569607000808808313462872867812749377748220q^{49} \) \(\mathstrut -\mathstrut 8993599813445960529795685588193052695282052910939102080q^{51} \) \(\mathstrut +\mathstrut 12450863873285726446941747254985680826918117392844470176q^{52} \) \(\mathstrut +\mathstrut 1380721489513428759527937305946915244571081819618418480q^{54} \) \(\mathstrut +\mathstrut 86716751505127419669577189864656813143075791367545723200q^{55} \) \(\mathstrut -\mathstrut 410655148353071807815217561752202738362370559954491547384q^{57} \) \(\mathstrut +\mathstrut 1171127646996109205778370152132525033757099595854063443360q^{58} \) \(\mathstrut -\mathstrut 4554593355431768584543074712701226261422872417617275398400q^{60} \) \(\mathstrut +\mathstrut 4552152490922647485493920930203353370116723196876970427240q^{61} \) \(\mathstrut -\mathstrut 18340670222945277450481852597884877177550760958776639152904q^{63} \) \(\mathstrut +\mathstrut 30281219638275425893507737167512138061029087969644636247040q^{64} \) \(\mathstrut -\mathstrut 73446637659820047047259347339723389117534541697924310768800q^{66} \) \(\mathstrut +\mathstrut 108802231400777081380268556166029877921173626685759369971416q^{67} \) \(\mathstrut -\mathstrut 255718829710356626829923504360603133388502621634044634870720q^{69} \) \(\mathstrut +\mathstrut 559303866272797397220431985027879540776975892234361655006400q^{70} \) \(\mathstrut -\mathstrut 561110698242036073669580259260779527574289380077856046595840q^{72} \) \(\mathstrut -\mathstrut 569085806526237236378057540729119438030642048917813502604504q^{73} \) \(\mathstrut +\mathstrut 2290039066363366330022806756651688579736177808604861676211500q^{75} \) \(\mathstrut -\mathstrut 5532330994825480968263901289000933629970925314426608479594720q^{76} \) \(\mathstrut +\mathstrut 9655803402636036605327159547820723686984585271634655943687200q^{78} \) \(\mathstrut -\mathstrut 22640121063621617622122249693012788180804867706114977596801800q^{79} \) \(\mathstrut +\mathstrut 37075761484886132865783336331999338158569856937859957696374420q^{81} \) \(\mathstrut -\mathstrut 69993225281309073377388502634775301823581628014590259964399040q^{82} \) \(\mathstrut +\mathstrut 62923532655099413129084384942812878939798728172266572844745120q^{84} \) \(\mathstrut -\mathstrut 142181474118416523657627044760532405955688084516779285440262400q^{85} \) \(\mathstrut +\mathstrut 23785411541262749066239132616113250012236593481925882591047200q^{87} \) \(\mathstrut +\mathstrut 345107275964501391166111220047509272448066379695588836103893760q^{88} \) \(\mathstrut -\mathstrut 1925479853343216377261941955721474942915647264800935046773530400q^{90} \) \(\mathstrut +\mathstrut 1225124508801982757577911377627409097047306370806522445345728240q^{91} \) \(\mathstrut -\mathstrut 2776404525956613483290023288082668840477640965472850083253548184q^{93} \) \(\mathstrut +\mathstrut 1658662465458978832407333757013771498132481417946327912207224960q^{94} \) \(\mathstrut -\mathstrut 3771017263293375391290634333996451541183976624371029742095907840q^{96} \) \(\mathstrut +\mathstrut 818755932265886448325223871671724131911117159175492830487918056q^{97} \) \(\mathstrut +\mathstrut 3118093180125811439250837213823663221313339534064003298574718400q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{65}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.65.b.a \(20\) \(77.821\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-1\!\cdots\!92\) \(0\) \(68\!\cdots\!76\) \(q+\beta _{1}q^{2}+(-71037898477915+13312\beta _{1}+\cdots)q^{3}+\cdots\)