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Properties

Label 12.22
Level 12
Weight 22
Dimension 43
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 176
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(176\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(12))\).

Total New Old
Modular forms 89 47 42
Cusp forms 79 43 36
Eisenstein series 10 4 6

Trace form

\( 43 q - 59049 q^{3} + 1212040 q^{4} + 17559810 q^{5} - 73477608 q^{6} + 791583864 q^{7} + 15323110971 q^{9} + O(q^{10}) \) \( 43 q - 59049 q^{3} + 1212040 q^{4} + 17559810 q^{5} - 73477608 q^{6} + 791583864 q^{7} + 15323110971 q^{9} + 70993722608 q^{10} - 112222937772 q^{11} + 230311800264 q^{12} - 725726689846 q^{13} - 2367628113510 q^{15} - 3296861950688 q^{16} + 2953244684214 q^{17} - 38138435545488 q^{18} + 25208162419020 q^{19} - 7103241137688 q^{21} + 345245332418448 q^{22} + 157775918327784 q^{23} + 162733136355360 q^{24} - 2435622081669483 q^{25} - 205891132094649 q^{27} + 3010485857135664 q^{28} - 4359534278069718 q^{29} + 5225832293639088 q^{30} + 3420045112432992 q^{31} - 4927403988048540 q^{33} - 11653770049992256 q^{34} + 58943170624401360 q^{35} - 18580578856893912 q^{36} - 25597840292902990 q^{37} + 21271071576651570 q^{39} - 89660451263290816 q^{40} - 58021202638110690 q^{41} - 196777060056297264 q^{42} + 91890557649844404 q^{43} + 551884209200145186 q^{45} - 24590270471085024 q^{46} + 639021428445851856 q^{47} - 1070121602451491040 q^{48} - 720260396448882941 q^{49} + 76201133615357022 q^{51} + 1474695233111072240 q^{52} - 605389055944970862 q^{53} - 107978656785090264 q^{54} + 223229472927915960 q^{55} - 2442884146037356212 q^{57} + 9260173307858336144 q^{58} + 111533213628510372 q^{59} + 6491621502020133696 q^{60} - 19491067201098601510 q^{61} + 2760082269078505464 q^{63} - 2949437838551773568 q^{64} - 15411720181369637700 q^{65} + 1836224451373338192 q^{66} + 5308269714319267356 q^{67} + 27358457849854520520 q^{69} - 24886444039106795232 q^{70} + 31114565784489756600 q^{71} - 27969226308253542336 q^{72} + 99199950295188522446 q^{73} - 67005681755538219975 q^{75} + 22386121373924673552 q^{76} + 8172031342996112544 q^{77} + 76385487692811283152 q^{78} - 115367151634837499856 q^{79} - 439745179763386019637 q^{81} + 1864686882869863520 q^{82} + 224057353676040396684 q^{83} + 311685180307346738352 q^{84} - 106440038069048215004 q^{85} - 7791544403279033886 q^{87} + 15063645347500158144 q^{88} + 751807239847095025710 q^{89} - 159737520743388593232 q^{90} - 697445725818940231920 q^{91} + 107616993980455324464 q^{93} + 242051617770611035200 q^{94} + 519788551712918229000 q^{95} - 1187951481218430818688 q^{96} - 1385685814566059051914 q^{97} - 391297188857803294572 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(12))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
12.22.a \(\chi_{12}(1, \cdot)\) 12.22.a.a 1 1
12.22.a.b 2
12.22.b \(\chi_{12}(11, \cdot)\) 12.22.b.a 40 1

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)