Properties

Label 3.35.b
Level 3
Weight 35
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 10
Newforms 1
Sturm bound 11
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 35 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{35}(3, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 10 10 0
Eisenstein series 2 2 0

Trace form

\(10q \) \(\mathstrut +\mathstrut 119369106q^{3} \) \(\mathstrut -\mathstrut 55582533344q^{4} \) \(\mathstrut -\mathstrut 9250224859872q^{6} \) \(\mathstrut -\mathstrut 123569771565772q^{7} \) \(\mathstrut +\mathstrut 4787501147541018q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 119369106q^{3} \) \(\mathstrut -\mathstrut 55582533344q^{4} \) \(\mathstrut -\mathstrut 9250224859872q^{6} \) \(\mathstrut -\mathstrut 123569771565772q^{7} \) \(\mathstrut +\mathstrut 4787501147541018q^{9} \) \(\mathstrut -\mathstrut 2611205560422720q^{10} \) \(\mathstrut +\mathstrut 1839088058193784224q^{12} \) \(\mathstrut +\mathstrut 3639874363106470052q^{13} \) \(\mathstrut +\mathstrut 73840351311049043520q^{15} \) \(\mathstrut -\mathstrut 458913568062658993664q^{16} \) \(\mathstrut +\mathstrut 4458031837811233600320q^{18} \) \(\mathstrut -\mathstrut 18128087575667617007644q^{19} \) \(\mathstrut +\mathstrut 47155216574801503272132q^{21} \) \(\mathstrut -\mathstrut 82944038352793331672640q^{22} \) \(\mathstrut -\mathstrut 409540832361157949627904q^{24} \) \(\mathstrut -\mathstrut 306157881917435527620230q^{25} \) \(\mathstrut -\mathstrut 5188422304885629117270366q^{27} \) \(\mathstrut +\mathstrut 1200257625823339935397952q^{28} \) \(\mathstrut +\mathstrut 4536084230702466968226240q^{30} \) \(\mathstrut -\mathstrut 16210124253435972809624620q^{31} \) \(\mathstrut +\mathstrut 126080615773751026110338880q^{33} \) \(\mathstrut -\mathstrut 95987113410493892068003584q^{34} \) \(\mathstrut -\mathstrut 3778740843166378351675872q^{36} \) \(\mathstrut +\mathstrut 1107877531995608327024550788q^{37} \) \(\mathstrut -\mathstrut 1478567172848906073011055372q^{39} \) \(\mathstrut +\mathstrut 1263325098820483891139005440q^{40} \) \(\mathstrut -\mathstrut 1100302459230379163303563200q^{42} \) \(\mathstrut -\mathstrut 9626706570211152095714911228q^{43} \) \(\mathstrut +\mathstrut 6764773545409610284732206720q^{45} \) \(\mathstrut -\mathstrut 27597232473865615892091763584q^{46} \) \(\mathstrut -\mathstrut 8343379363160137604055750144q^{48} \) \(\mathstrut +\mathstrut 123592722368423574378839845566q^{49} \) \(\mathstrut -\mathstrut 154249157901217791265339790592q^{51} \) \(\mathstrut +\mathstrut 364968511672502550561914224448q^{52} \) \(\mathstrut -\mathstrut 627476296349871988055293152672q^{54} \) \(\mathstrut +\mathstrut 613243149395194155294476807040q^{55} \) \(\mathstrut -\mathstrut 200956522080425270978267102412q^{57} \) \(\mathstrut +\mathstrut 911704545930429232428533728320q^{58} \) \(\mathstrut -\mathstrut 5328764870697498499759490872320q^{60} \) \(\mathstrut +\mathstrut 3721644688213000805892336114020q^{61} \) \(\mathstrut -\mathstrut 17793115140162074693090527345068q^{63} \) \(\mathstrut +\mathstrut 31237929890100178456062152876032q^{64} \) \(\mathstrut -\mathstrut 56522434211150051720831749496640q^{66} \) \(\mathstrut +\mathstrut 64610860820592975458220110976548q^{67} \) \(\mathstrut -\mathstrut 75655347603668350171840261441152q^{69} \) \(\mathstrut +\mathstrut 173956643092708582155719748059520q^{70} \) \(\mathstrut -\mathstrut 251655858465803757687636471720960q^{72} \) \(\mathstrut +\mathstrut 219744563327934154882825652170292q^{73} \) \(\mathstrut -\mathstrut 496257346175691552817323610505790q^{75} \) \(\mathstrut +\mathstrut 755138601297458545349651061598016q^{76} \) \(\mathstrut -\mathstrut 1416035973322463045417779737274560q^{78} \) \(\mathstrut +\mathstrut 1282143700776175332608732687725076q^{79} \) \(\mathstrut -\mathstrut 1752271238163022185686811202609110q^{81} \) \(\mathstrut +\mathstrut 2617087107433191584283809414490240q^{82} \) \(\mathstrut -\mathstrut 3353754502177451840461431126935232q^{84} \) \(\mathstrut +\mathstrut 3064318591304040683100089841123840q^{85} \) \(\mathstrut -\mathstrut 1378895999771415686373632115051840q^{87} \) \(\mathstrut +\mathstrut 2890193643030846777850875310341120q^{88} \) \(\mathstrut -\mathstrut 3749676158586283582801263594857280q^{90} \) \(\mathstrut +\mathstrut 3328617839789463835132355588364424q^{91} \) \(\mathstrut -\mathstrut 913294458028957034010214182487068q^{93} \) \(\mathstrut -\mathstrut 1912224205137436189468854646420224q^{94} \) \(\mathstrut +\mathstrut 5756213457708614900907762734014464q^{96} \) \(\mathstrut -\mathstrut 11994339580278056229821837667722092q^{97} \) \(\mathstrut +\mathstrut 25463971047319347192017533065521280q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{35}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.35.b.a \(10\) \(21.968\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(119369106\) \(0\) \(-1\!\cdots\!72\) \(q+\beta _{1}q^{2}+(11936911+41\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)