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Properties

Label 21.12
Level 21
Weight 12
Dimension 124
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 384
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(384\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(21))\).

Total New Old
Modular forms 188 136 52
Cusp forms 164 124 40
Eisenstein series 24 12 12

Trace form

\( 124 q - 156 q^{2} + 240 q^{3} - 16270 q^{4} + 25926 q^{5} - 8748 q^{6} + 95858 q^{7} - 364362 q^{8} - 95316 q^{9} + O(q^{10}) \) \( 124 q - 156 q^{2} + 240 q^{3} - 16270 q^{4} + 25926 q^{5} - 8748 q^{6} + 95858 q^{7} - 364362 q^{8} - 95316 q^{9} - 1006992 q^{10} + 2168754 q^{11} + 1044816 q^{12} - 4578450 q^{13} + 911016 q^{14} + 7289892 q^{15} + 4986418 q^{16} - 20915472 q^{17} - 57373326 q^{18} + 9829158 q^{19} + 208941924 q^{20} - 25021878 q^{21} - 281709120 q^{22} - 33942648 q^{23} + 219544560 q^{24} + 125172514 q^{25} - 85963782 q^{26} - 28697814 q^{27} - 778785110 q^{28} + 55035312 q^{29} + 875231910 q^{30} + 1065240054 q^{31} + 141397422 q^{32} - 1210649112 q^{33} - 2998330044 q^{34} - 188269086 q^{35} + 3154221258 q^{36} - 522351176 q^{37} + 2863053174 q^{38} + 1146290466 q^{39} - 2321750904 q^{40} - 5108017836 q^{41} + 917605998 q^{42} + 451400800 q^{43} + 8634464472 q^{44} + 3069855756 q^{45} - 5226631068 q^{46} - 9119839962 q^{47} - 3744664992 q^{48} + 534491554 q^{49} + 12401784402 q^{50} + 5012082180 q^{51} + 18419178168 q^{52} - 4383832044 q^{53} + 9890068410 q^{54} - 31418985240 q^{55} - 50897831022 q^{56} - 16794190368 q^{57} + 29905504488 q^{58} + 41910542316 q^{59} + 21727277460 q^{60} - 10966065750 q^{61} - 72062486652 q^{62} - 5074714218 q^{63} + 93180789446 q^{64} + 34131921774 q^{65} + 11522305242 q^{66} - 10589572102 q^{67} - 85753019328 q^{68} - 30094945416 q^{69} - 128723772144 q^{70} + 37983065484 q^{71} + 148141686510 q^{72} + 118013887524 q^{73} - 27646219962 q^{74} - 29432293854 q^{75} + 61658709192 q^{76} - 3437989608 q^{77} - 130373153568 q^{78} - 200997166690 q^{79} - 167865734184 q^{80} + 47387357496 q^{81} + 188065740024 q^{82} + 327381542364 q^{83} + 442338340908 q^{84} - 28003464792 q^{85} - 432070908090 q^{86} - 190169349156 q^{87} - 629948449812 q^{88} - 31530231600 q^{89} - 21392271720 q^{90} + 200773225944 q^{91} + 670589880576 q^{92} + 350879210094 q^{93} + 7746670920 q^{94} + 135130970034 q^{95} + 247006314036 q^{96} + 489883921188 q^{97} - 352347190938 q^{98} - 885463275060 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.12.a \(\chi_{21}(1, \cdot)\) 21.12.a.a 1 1
21.12.a.b 1
21.12.a.c 3
21.12.a.d 3
21.12.a.e 4
21.12.c \(\chi_{21}(20, \cdot)\) 21.12.c.a 28 1
21.12.e \(\chi_{21}(4, \cdot)\) 21.12.e.a 14 2
21.12.e.b 16
21.12.g \(\chi_{21}(5, \cdot)\) 21.12.g.a 2 2
21.12.g.b 52

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)