Properties

Label 1.34.a
Level 1
Weight 34
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 34 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_0(1))\).

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

Trace form

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

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.34.a.a \(2\) \(6.898\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-121680\) \(37919880\) \(-181061536500\) \(-6\!\cdots\!00\) \(+\) \(q+(-60840-\beta )q^{2}+(18959940+312\beta )q^{3}+\cdots\)