Properties

Label 3.67.b
Level 3
Weight 67
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 21
Newforms 2
Sturm bound 22
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 67 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(22\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{67}(3, [\chi])\).

Total New Old
Modular forms 23 23 0
Cusp forms 21 21 0
Eisenstein series 2 2 0

Trace form

\(21q \) \(\mathstrut -\mathstrut 688084969601007q^{3} \) \(\mathstrut -\mathstrut 800685737036149288416q^{4} \) \(\mathstrut -\mathstrut 36458623571791371420365280q^{6} \) \(\mathstrut -\mathstrut 2702047559314351527601390326q^{7} \) \(\mathstrut +\mathstrut 45992711688628379060241515442429q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(21q \) \(\mathstrut -\mathstrut 688084969601007q^{3} \) \(\mathstrut -\mathstrut 800685737036149288416q^{4} \) \(\mathstrut -\mathstrut 36458623571791371420365280q^{6} \) \(\mathstrut -\mathstrut 2702047559314351527601390326q^{7} \) \(\mathstrut +\mathstrut 45992711688628379060241515442429q^{9} \) \(\mathstrut -\mathstrut 783798592344000703899756417518400q^{10} \) \(\mathstrut +\mathstrut 313126982154513861252459017125509792q^{12} \) \(\mathstrut +\mathstrut 7097926243613473019176328483636438706q^{13} \) \(\mathstrut +\mathstrut 291841906843973945390453919652713854400q^{15} \) \(\mathstrut +\mathstrut 40614425652107854809231797245756798419456q^{16} \) \(\mathstrut -\mathstrut 1327598375030727473316959111629621787325120q^{18} \) \(\mathstrut -\mathstrut 3026253719358562084411563912125371924232382q^{19} \) \(\mathstrut +\mathstrut 94405468614025363801741480774192639322611842q^{21} \) \(\mathstrut -\mathstrut 19209253722854761211546865955725969475475520q^{22} \) \(\mathstrut -\mathstrut 8536939678857788536491103872952212579880680960q^{24} \) \(\mathstrut -\mathstrut 17147961692404127551588071265216534139284367475q^{25} \) \(\mathstrut +\mathstrut 386598848155105460060789059338932209496472438297q^{27} \) \(\mathstrut -\mathstrut 996205777307676532598553893751207432016740832704q^{28} \) \(\mathstrut -\mathstrut 13469561117532417280775174235598750536019791067200q^{30} \) \(\mathstrut -\mathstrut 14654619455858594306346020767449979844677242053478q^{31} \) \(\mathstrut +\mathstrut 76031443883614128882573745917963369573166525959360q^{33} \) \(\mathstrut -\mathstrut 607578292754219603165333260413176675880514014447360q^{34} \) \(\mathstrut -\mathstrut 895023811463443645999922679504197455464847252142304q^{36} \) \(\mathstrut +\mathstrut 20017769738379707622473792283398210981888313792060834q^{37} \) \(\mathstrut +\mathstrut 66636801091900395134689625163950363064549067501207818q^{39} \) \(\mathstrut -\mathstrut 164157270356735970397207190518038139497893424374707200q^{40} \) \(\mathstrut -\mathstrut 362475530834094311762041222130355899146344066985844160q^{42} \) \(\mathstrut +\mathstrut 1750683764257600519072611471115188115349321260457464146q^{43} \) \(\mathstrut +\mathstrut 2893961767142107219663835709681578507068881328379222400q^{45} \) \(\mathstrut -\mathstrut 9354105762324374445425328051923657080564209708616152960q^{46} \) \(\mathstrut +\mathstrut 13817528706178021501150679795616158657279365440273074688q^{48} \) \(\mathstrut +\mathstrut 215128591806865673017752231478506065368765042180747979727q^{49} \) \(\mathstrut +\mathstrut 244898096463243383440025305755038369424109352434412094720q^{51} \) \(\mathstrut -\mathstrut 1518265416812062984196689570755057404628632785205545096896q^{52} \) \(\mathstrut -\mathstrut 386962012382976993771518038850875450617071434969909598880q^{54} \) \(\mathstrut +\mathstrut 1313751320608480207642793301222628514163843327983665564800q^{55} \) \(\mathstrut +\mathstrut 19099434894617664662341642357315366358083446634989076587354q^{57} \) \(\mathstrut -\mathstrut 100361163480954821917122043432794223233970822326053950441920q^{58} \) \(\mathstrut +\mathstrut 188095594234899922680776576921513155518384075353356847385600q^{60} \) \(\mathstrut +\mathstrut 113336939225624355656015939981441781500323155005015569459602q^{61} \) \(\mathstrut +\mathstrut 867289963069300891393622628986175964602499204766868854587866q^{63} \) \(\mathstrut -\mathstrut 3834144414815230440260964913649794504762796578058449640349696q^{64} \) \(\mathstrut +\mathstrut 8309681532541455738248790801869091701653966958238676467844800q^{66} \) \(\mathstrut -\mathstrut 6049423726944633447191209261927909749694186597555115893152606q^{67} \) \(\mathstrut +\mathstrut 26395268384310228436148510386607667671115625880708467370286720q^{69} \) \(\mathstrut -\mathstrut 53673269104481250134670425876769459429788829882429608923689600q^{70} \) \(\mathstrut +\mathstrut 135607917285688125946137613885497485690645144416066370695173120q^{72} \) \(\mathstrut -\mathstrut 178147484335790867284195105212850456640968756739384871647383494q^{73} \) \(\mathstrut +\mathstrut 48500659963334295446540398772268295428047679651616767953046825q^{75} \) \(\mathstrut -\mathstrut 149865848814600171328195720360577671384923125006177154868747968q^{76} \) \(\mathstrut +\mathstrut 42333034554100439516880814575759716324771014654582144994836800q^{78} \) \(\mathstrut +\mathstrut 444494431904136800989393001687173188707366949918924051811195578q^{79} \) \(\mathstrut -\mathstrut 1714755033212258332948685465092598786715301424884224614290293339q^{81} \) \(\mathstrut +\mathstrut 9780548955253740491517774427483475844287869484539284101189512320q^{82} \) \(\mathstrut -\mathstrut 23209425572238177028755357107740308790467159790146246204677483712q^{84} \) \(\mathstrut +\mathstrut 15725476767553808561610465539289169056529282358913795578981260800q^{85} \) \(\mathstrut -\mathstrut 20361537149674837364457194316410702650457831770981879709222020800q^{87} \) \(\mathstrut +\mathstrut 43127341602231234631198337877354797375008485566513397535855918080q^{88} \) \(\mathstrut -\mathstrut 68986845993042571618317468832763287342807845905185213796199009600q^{90} \) \(\mathstrut +\mathstrut 3262721652025066881755116254518958419295537752131404627143858724q^{91} \) \(\mathstrut +\mathstrut 165867495181307153265816567053181483924867691908493681948316622546q^{93} \) \(\mathstrut -\mathstrut 243292275786183398644891798798613800120302016678942850492866824960q^{94} \) \(\mathstrut +\mathstrut 1707340756716414995397633331453898170371668874444383803046536028160q^{96} \) \(\mathstrut -\mathstrut 1800313724485416009736937253676448843389370135068996806872381547606q^{97} \) \(\mathstrut +\mathstrut 1311784025950014883691036763145966005164166837426590048709685526400q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{67}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.67.b.a \(1\) \(82.760\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-5\!\cdots\!23\) \(0\) \(-1\!\cdots\!14\) \(q-3^{33}q^{3}+2^{66}q^{4}+\cdots\)
3.67.b.b \(20\) \(82.760\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(48\!\cdots\!16\) \(0\) \(12\!\cdots\!88\) \(q+\beta _{1}q^{2}+(243548779847726+15513\beta _{1}+\cdots)q^{3}+\cdots\)