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Properties

Label 3.35
Level 3
Weight 35
Dimension 10
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 23
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 35 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(23\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{35}(\Gamma_1(3))\).

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{35}^{\mathrm{new}}(\Gamma_1(3))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3.35.b \(\chi_{3}(2, \cdot)\) 3.35.b.a 10 1