Properties

Label 1.34
Level 1
Weight 34
Dimension 2
Nonzero newspaces 1
Newforms 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 34 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(1))\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 0
Eisenstein series 1 1 0

Trace form

\( 2q - 121680q^{2} + 37919880q^{3} + 14652233984q^{4} - 181061536500q^{5} - 9928922193216q^{6} - 67153080066800q^{7} - 2818750585098240q^{8} - 8021136954970854q^{9} + O(q^{10}) \) \( 2q - 121680q^{2} + 37919880q^{3} + 14652233984q^{4} - 181061536500q^{5} - 9928922193216q^{6} - 67153080066800q^{7} - 2818750585098240q^{8} - 8021136954970854q^{9} + 35542592216532000q^{10} + 133871815441914264q^{11} + 1205235433330467840q^{12} - 2981610478259443940q^{13} - 15496641262468340352q^{14} - 11085280069139874000q^{15} + 195605979111894351872q^{16} - 79361149261175525340q^{17} + 198985322728543319280q^{18} - 1360696443041697171800q^{19} - 4310900037459183168000q^{20} + 4836438843082801141824q^{21} + 24751741840613395122240q^{22} + 26163854053674631579440q^{23} - 100235518588319710003200q^{24} - 191814088084783724781250q^{25} + 272731683634642092710304q^{26} - 272704742315639906405040q^{27} + 1890794991723644827125760q^{28} - 1674519971630399929109700q^{29} + 1829469606462141559632000q^{30} - 6238301225723632337095616q^{31} - 5708163006744585940500480q^{32} - 7725507376265263259943840q^{33} + 69860790536166916073075808q^{34} - 13581143663546216842308000q^{35} - 23595755096197135608576768q^{36} - 104802741516758180098173620q^{37} - 36544090911856460663722560q^{38} - 85026272438019668836783248q^{39} + 405758480738092701742080000q^{40} + 277566613022002182732188244q^{41} - 409610685367579027895216640q^{42} + 1567661189367072113768291800q^{43} - 3022085914387766085808346112q^{44} + 435982958561646097146265500q^{45} - 5613550634763385681470869376q^{46} + 5421061461431251260476972640q^{47} + 9331035686759324258712944640q^{48} + 2489799365888888933444851314q^{49} + 7229107516344249428363250000q^{50} - 21794809591439435388668624496q^{51} - 32956722688372988680703091200q^{52} - 26867414785542903092975171220q^{53} + 84050074928235529084016073600q^{54} + 20908570805489145209222682000q^{55} - 25575237795171758759822131200q^{56} + 11431882183748158902465090720q^{57} + 250532370716581201796821222560q^{58} - 305786409635298433026663995400q^{59} - 221757467882938689123571968000q^{60} - 5745893983413264859067362436q^{61} - 424581887479352364037004290560q^{62} + 500999494400792409792776544720q^{63} + 864365322360380859973709594624q^{64} + 361623311364964256200313721000q^{65} + 583558358556830038058269663488q^{66} + 1598906337224495341750209565960q^{67} - 8494558579722382470601861086720q^{68} + 1750848530317427976275742443712q^{69} + 1775546165763388432770973344000q^{70} - 2669761937956104715736810084976q^{71} + 9530438520123487645446231060480q^{72} + 946314321191998870965166536340q^{73} + 1457936998080019494211346192928q^{74} - 2251234781189208709982677125000q^{75} + 4551314657470802548563162035200q^{76} - 30864620292716415864215760033600q^{77} + 18267352963262685465124679337600q^{78} - 8535199972765636469730106191200q^{79} - 35800819471604723635001769984000q^{80} + 18372400450705101408694430349042q^{81} + 62171822095602398237444019107040q^{82} + 29072605803747945444403983322920q^{83} + 49469534061147727842067908599808q^{84} + 72477213859794605306963311287000q^{85} - 312696885737578501917214826406336q^{86} - 78129025791401437906177732680720q^{87} + 13282372192867492753038509752320q^{88} + 132719467655604316264938597726900q^{89} - 98726386114587723068546425404000q^{90} + 26902102147452358410548887211744q^{91} + 681044992402323869436382557788160q^{92} + 132607664882695458799488635592960q^{93} - 450506433888867898835049561530112q^{94} + 3378716387067841884487537110000q^{95} - 793791282556560211499025092837376q^{96} - 367787330930535727150839877856060q^{97} + 1163527978168280943548587223169840q^{98} - 926100695332764780030656940070728q^{99} + O(q^{100}) \)

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(1))\)

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
1.34.a \(\chi_{1}(1, \cdot)\) 1.34.a.a 2 1