Properties

Label 3.30
Level 3
Weight 30
Dimension 5
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 20
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 30 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(\Gamma_1(3))\).

Total New Old
Modular forms 11 5 6
Cusp forms 9 5 4
Eisenstein series 2 0 2

Trace form

\( 5q - 33666q^{2} + 4782969q^{3} + 2317310516q^{4} + 35680523406q^{5} + 269788149414q^{6} + 3367889703880q^{7} + 7778720393448q^{8} + 114383962274805q^{9} + O(q^{10}) \) \( 5q - 33666q^{2} + 4782969q^{3} + 2317310516q^{4} + 35680523406q^{5} + 269788149414q^{6} + 3367889703880q^{7} + 7778720393448q^{8} + 114383962274805q^{9} + 171907890247764q^{10} + 1366144892304492q^{11} + 9052308753172596q^{12} - 12361315731947402q^{13} - 226466432160780432q^{14} + 168864135184609254q^{15} + 1383871481050014224q^{16} + 768762053759550042q^{17} - 770170094788717026q^{18} - 4254151285566720908q^{19} + 21441848131981844664q^{20} - 9183599600261630904q^{21} - 4977228299716913976q^{22} + 1139319855427683480q^{23} - 31175841519160870104q^{24} + 694299657773167892171q^{25} - 1317631965027289742460q^{26} + 109418989131512359209q^{27} - 1111552332222024139040q^{28} - 573727225266369721626q^{29} - 4024708806292033917564q^{30} + 874575436715357515744q^{31} + 21632826338162898164640q^{32} - 4786770519802149245316q^{33} + 62778493618984917998172q^{34} - 101496238049117183741520q^{35} + 53012631728230581669876q^{36} - 147536219660404225059890q^{37} + 11173433641677487992696q^{38} + 147700288454792470991694q^{39} + 190619318209073462111088q^{40} + 258354660989087410026354q^{41} - 69036826488487354584720q^{42} - 1139190453328713361541876q^{43} - 2700808870924343843995920q^{44} + 816255928643440161317166q^{45} + 4307698246997613179416464q^{46} - 2046083847613299533692752q^{47} + 7731512664581516318537616q^{48} + 7716540176957078860188093q^{49} - 27779742358441462465090206q^{50} + 6579623188098677211684930q^{51} + 26920485456487672207829272q^{52} - 12682341544407995141709570q^{53} + 6171887500952086133542854q^{54} + 9614686856738973448034376q^{55} - 151546885676638941943728960q^{56} + 54533630073316307689431396q^{57} + 62309777277870418889785572q^{58} - 141949687119373427106547812q^{59} + 322471929035301163167005496q^{60} + 229031641409934422545419238q^{61} - 511290685975746871273745280q^{62} + 77046513766862820526948680q^{63} + 74885603748557304530177600q^{64} - 192344861799374044671037212q^{65} + 80607976862733238471344360q^{66} + 134076035712199162011310372q^{67} + 74014674281940772548762408q^{68} + 16126077307043010049778808q^{69} + 440687991555250165196710560q^{70} + 103908489604981772087058120q^{71} + 177952172006082467739495528q^{72} - 667898688881482633186946990q^{73} - 1114072846287045694094746092q^{74} - 2296949022983924978296193001q^{75} - 2630801882986850322878187632q^{76} + 3232213895350288890376395360q^{77} - 8025127102096756434155722572q^{78} + 2176133411918622187383634960q^{79} + 29515119880053891203760596064q^{80} + 2616738165136802686067557605q^{81} - 22434006880815823798209744660q^{82} + 35005942823392994902796883252q^{83} - 28025681310219792325631719968q^{84} - 29038992201508758500243727108q^{85} - 4181889596778973632312603768q^{86} + 12078163448987889439785924702q^{87} - 8315606904626810628324302112q^{88} - 5975598877697204259248128158q^{89} + 3932701126568311148100957204q^{90} + 60722805575186877699993847664q^{91} - 25992440511160073345040324000q^{92} - 45419872256566033528410261120q^{93} + 34317595302438574344228368544q^{94} - 33252863635760230502810983176q^{95} + 77106242152821220141026100896q^{96} - 118517998798721882645128790678q^{97} + 17295844568260655533195668942q^{98} + 31253013164654910497407984812q^{99} + O(q^{100}) \)

Decomposition of \(S_{30}^{\mathrm{new}}(\Gamma_1(3))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
3.30.a \(\chi_{3}(1, \cdot)\) 3.30.a.a 2 1
3.30.a.b 3

Decomposition of \(S_{30}^{\mathrm{old}}(\Gamma_1(3))\) into lower level spaces

\( S_{30}^{\mathrm{old}}(\Gamma_1(3)) \cong \) \(S_{30}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)