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Properties

Label 21.39
Level 21
Weight 39
Dimension 426
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 1248
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 39 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(1248\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{39}(\Gamma_1(21))\).

Total New Old
Modular forms 620 434 186
Cusp forms 596 426 170
Eisenstein series 24 8 16

Trace form

\( 426 q - 932776662 q^{3} + 2299037429114 q^{4} - 39631087093926 q^{5} + 967222409360250 q^{6} + 20269838802934058 q^{7} + 828002231222727426 q^{8} - 579213056841151536 q^{9} + O(q^{10}) \) \( 426 q - 932776662 q^{3} + 2299037429114 q^{4} - 39631087093926 q^{5} + 967222409360250 q^{6} + 20269838802934058 q^{7} + 828002231222727426 q^{8} - 579213056841151536 q^{9} + 25400485471539530508 q^{10} + 329928792876899680134 q^{11} + 1627027108328576714862 q^{12} - 1443153780525378007630 q^{13} - 35909614804852872134664 q^{14} - 1756424112174593432592 q^{15} + 301870465258674939412674 q^{16} + 306434696659540981410192 q^{17} - 4944937398975833153384892 q^{18} + 3527192894494709324252258 q^{19} - 28386139330144009755128952 q^{21} - 13168399197829569561639756 q^{22} + 244899200059674905479667424 q^{23} - 950169122586393476605756494 q^{24} + 966466192960230176797950228 q^{25} + 1697529646711137648881325546 q^{26} - 8452606555369629806190935820 q^{27} + 1914317726189460931513928106 q^{28} + 27551159179528390264671554388 q^{29} - 16616428592743047546360535296 q^{30} + 45751177076945627833361443910 q^{31} - 348577093165214283199098187722 q^{32} + 495279992294835170723912927634 q^{33} - 1159269484802781156193439599008 q^{34} + 22545584747091764056759191810 q^{35} - 11121936391018723730521212585690 q^{36} + 588445162065475600586361989440 q^{37} - 2444658392733517629922209446946 q^{38} - 9875622670106121158722771660614 q^{39} + 399438840208337073248132322096 q^{40} - 884381061828643499826983360232 q^{42} - 66207976201637214985747531745804 q^{43} + 212765918080235177287645279281528 q^{44} + 80341896985887272511288358018962 q^{45} - 349388867162734879384737538798956 q^{46} + 297478609907953150379536377169362 q^{47} - 501384265236408514939340658616362 q^{48} + 2769764434753539676038956251886304 q^{49} - 2130280027280708596942850971084794 q^{50} + 1637843199765457912200759539134776 q^{51} - 4879461258073519236543727123006216 q^{52} + 3187964821966036899239286661604772 q^{53} - 3240342623656883513575855572103524 q^{54} - 2452324380342864741301553789679924 q^{55} + 2207600581343990983478067925993266 q^{56} - 7568880866524125737420959272757140 q^{57} + 27958744686180286114540700130672768 q^{58} - 42335590663870057033850971106213484 q^{59} + 58507495332450704497883477563767276 q^{60} - 25665419259896032170288914985968698 q^{61} + 61367191284714717554850887841536550 q^{63} - 231010101719928948486852824828080954 q^{64} + 79490046532037704041830856476222178 q^{65} - 178958452302662395813800742509845400 q^{66} + 386291820449248008245672943416721462 q^{67} - 495755326196945813827659313510481628 q^{68} + 487487182471106143386337382590361136 q^{69} - 487233895775876400003630016260722460 q^{70} - 301441657561749375179533693644176616 q^{71} + 3414193773912700100439497433246293166 q^{72} - 1707367141707644375301055043445704788 q^{73} - 2912398169962322322544992744937379886 q^{74} + 1362419108226811405221279047227284540 q^{75} - 2961137957869514963072689854341259796 q^{76} - 1850747872333751934093409387495500504 q^{77} + 9566314160667874045639952727757074216 q^{78} - 9568911415254273911822191568009154030 q^{79} + 17524309749719525539706976348715001088 q^{80} - 1271620213992354350162757623461305552 q^{81} - 14695599213624737443188055398656263380 q^{82} - 10143175311232292254257259969922334702 q^{84} - 21394494429425132047185180789890288808 q^{85} + 25084314515531042093905259282601661554 q^{86} + 27828421892247466528322625936214369860 q^{87} - 138219220146781299977699770398856251480 q^{88} - 11500296475075344214524986710086900732 q^{89} + 170071920803139027825633638789508062628 q^{90} - 60754401300041271938934021365727945892 q^{91} + 95500549819525511220645479912884695756 q^{92} - 3497111140349644686647226504556386432 q^{93} - 342788858096992863364262218542042571812 q^{94} + 386302955834794322122093094992005036282 q^{95} + 109253995905765907420854364827706580166 q^{96} + 59172625167039046068497185645251004040 q^{97} + 192801468039615831155093134493347018458 q^{98} + 876531269999774383217638858623862314144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{39}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.39.b \(\chi_{21}(8, \cdot)\) 21.39.b.a 76 1
21.39.d \(\chi_{21}(13, \cdot)\) 21.39.d.a 50 1
21.39.f \(\chi_{21}(10, \cdot)\) 21.39.f.a 50 2
21.39.f.b 52
21.39.h \(\chi_{21}(2, \cdot)\) 21.39.h.a 2 2
21.39.h.b 196

Decomposition of \(S_{39}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{39}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{39}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{39}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)