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Properties

Label 3.41
Level 3
Weight 41
Dimension 12
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 27
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 41 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(27\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{41}(\Gamma_1(3))\).

Total New Old
Modular forms 14 14 0
Cusp forms 12 12 0
Eisenstein series 2 2 0

Trace form

\( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 8471862485327952 q^{6} - 94341749124766584 q^{7} - 23605502262041939220 q^{9} + O(q^{10}) \) \( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 8471862485327952 q^{6} - 94341749124766584 q^{7} - 23605502262041939220 q^{9} - 129384136354706290080 q^{10} - 4708039830028985428272 q^{12} + 704368845864154901976 q^{13} + 320935800901459838631840 q^{15} + 6054431850962872672227456 q^{16} + 10227710367381761273509920 q^{18} + 37616619688417835612151720 q^{19} - 179163719456723608834234728 q^{21} + 846315150249292772829325920 q^{22} - 18213480358094369517645250944 q^{24} + 8842265325510151276196474700 q^{25} - 70717074113738779393083858252 q^{27} + 469404222007499612173589889696 q^{28} - 207809636542026559976510503200 q^{30} - 914600368399753689553849145016 q^{31} + 157344642221562801276041757600 q^{33} - 14575908480758621487300381842304 q^{34} + 41100171486790863962401658870544 q^{36} + 5673106137824212681873457220696 q^{37} - 9206461430638842876438079090008 q^{39} + 50495897877443363581635475618560 q^{40} - 939238658319640212873301303645920 q^{42} + 1012654832326802922602871229857576 q^{43} + 196109968512215856818385626472000 q^{45} - 3082500781506234684371181468390336 q^{46} + 6532128822166367998693520969705088 q^{48} + 8498166150175390075155260408801892 q^{49} + 27565453699222767413826960590504832 q^{51} - 57328509042562386918101767400001504 q^{52} - 102847607224782098537542351912875792 q^{54} - 9637639495259752880102706884884800 q^{55} - 40307213604482059940636368892395464 q^{57} + 772129436848561910287203884295052320 q^{58} - 114385571579949295944121547557720320 q^{60} - 494443282701607071691140418439862696 q^{61} + 1379291076525018665154441723571240776 q^{63} - 6231783699524672226208093043936541696 q^{64} + 2652084094607847915810184973553481440 q^{66} + 5401062423529881431761320436868275176 q^{67} + 7110274695178254111533494284632123328 q^{69} + 516103243900107216646679160954379200 q^{70} - 27544975046740790141119542770107057920 q^{72} + 30000154498324943042431295514883418136 q^{73} + 43820294796704764666539599709819928500 q^{75} - 215478934792040263381331019050660960352 q^{76} + 234946633516471169601955850003339878560 q^{78} - 128704557118405295534397879672035334840 q^{79} + 473157359902659920298963194247360443532 q^{81} - 639159997421964256448917103585883414720 q^{82} + 1283288903941350744781821238287455403552 q^{84} - 1077142486191382871466217243736209678080 q^{85} + 1076668306862385320797179121273520148960 q^{87} - 2918662713596496795370587920448329114880 q^{88} + 6571793457940570799819318674019816438880 q^{90} - 9859184204686878150356379414618151910256 q^{91} + 11506410044121210986218054652959643683416 q^{93} - 16857264118330945289191940748512432348544 q^{94} + 53068562519213731340201280418423192237056 q^{96} - 41841010071967618660163746722085070705064 q^{97} + 54341076855402233475300783474292013590080 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{41}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.41.b \(\chi_{3}(2, \cdot)\) 3.41.b.a 12 1