↑

Properties

Label 91.11
Level 91
Weight 11
Dimension 3126
Nonzero newspaces 15
Newform subspaces 17
Sturm bound 7392
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 91 = 7 \cdot 13 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 17 \)
Sturm bound: \(7392\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(91))\).

Total New Old
Modular forms 3432 3234 198
Cusp forms 3288 3126 162
Eisenstein series 144 108 36

Trace form

\( 3126 q - 18 q^{2} + 468 q^{3} + 4078 q^{4} - 6684 q^{5} - 24 q^{6} + 56378 q^{7} - 215694 q^{8} - 111594 q^{9} + O(q^{10}) \) \( 3126 q - 18 q^{2} + 468 q^{3} + 4078 q^{4} - 6684 q^{5} - 24 q^{6} + 56378 q^{7} - 215694 q^{8} - 111594 q^{9} + 967296 q^{10} - 292956 q^{11} - 3162972 q^{12} + 2455440 q^{13} + 3793602 q^{14} - 3385068 q^{15} - 9621194 q^{16} - 5021688 q^{17} + 18991578 q^{18} - 5551516 q^{19} - 14467080 q^{20} + 8481036 q^{21} + 60951276 q^{22} + 3068280 q^{23} - 197664360 q^{24} - 65848246 q^{25} + 78955740 q^{26} + 189207456 q^{27} + 268216594 q^{28} + 101961024 q^{29} - 769726008 q^{30} - 83615192 q^{31} + 24697818 q^{32} + 130626936 q^{33} + 476511576 q^{34} + 417809520 q^{35} - 218034318 q^{36} + 483041580 q^{37} - 1057726116 q^{38} - 306120768 q^{39} + 1308975456 q^{40} + 81720996 q^{41} + 455424180 q^{42} + 967701188 q^{43} + 763106088 q^{44} - 540465984 q^{45} - 1675805268 q^{46} - 640503504 q^{47} + 769034952 q^{48} + 1045921166 q^{49} - 1262504634 q^{50} + 1729386648 q^{51} + 6502788508 q^{52} - 1253385336 q^{53} - 8081641956 q^{54} + 1981737996 q^{55} + 9705453774 q^{56} + 4797981168 q^{57} - 7651442796 q^{58} - 4077226872 q^{59} - 13904452980 q^{60} + 2396166672 q^{61} + 961703232 q^{62} + 7958700282 q^{63} + 3138504022 q^{64} - 19134041652 q^{65} - 21010027776 q^{66} + 12045456792 q^{67} + 33659190228 q^{68} + 16123205412 q^{69} - 4137225888 q^{70} - 9214169160 q^{71} - 39272782566 q^{72} - 842382664 q^{73} - 31027807068 q^{74} - 18635034552 q^{75} + 15277400816 q^{76} + 27227358672 q^{77} + 68396360856 q^{78} + 4745394472 q^{79} + 18658855140 q^{80} + 6848328774 q^{81} - 3790231344 q^{82} - 35890879488 q^{83} - 110492534064 q^{84} - 85581182856 q^{85} - 3657958704 q^{86} + 163827445824 q^{87} + 204925665072 q^{88} + 10171206324 q^{89} - 62588699516 q^{91} - 184691524284 q^{92} - 89451988788 q^{93} - 134940494544 q^{94} + 51935719620 q^{95} + 209755173132 q^{96} + 36293664664 q^{97} + 163072654674 q^{98} + 34857278532 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(91))\)

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
91.11.b \(\chi_{91}(90, \cdot)\) 91.11.b.a 1 1
91.11.b.b 1
91.11.b.c 88
91.11.d \(\chi_{91}(27, \cdot)\) 91.11.d.a 80 1
91.11.j \(\chi_{91}(8, \cdot)\) 91.11.j.a 140 2
91.11.l \(\chi_{91}(17, \cdot)\) 91.11.l.a 182 2
91.11.m \(\chi_{91}(3, \cdot)\) 91.11.m.a 182 2
91.11.n \(\chi_{91}(48, \cdot)\) 91.11.n.a 184 2
91.11.o \(\chi_{91}(40, \cdot)\) 91.11.o.a 160 2
91.11.p \(\chi_{91}(10, \cdot)\) 91.11.p.a 182 2
91.11.s \(\chi_{91}(12, \cdot)\) 91.11.s.a 184 2
91.11.t \(\chi_{91}(62, \cdot)\) 91.11.t.a 184 2
91.11.v \(\chi_{91}(68, \cdot)\) 91.11.v.a 182 2
91.11.x \(\chi_{91}(2, \cdot)\) 91.11.x.a 364 4
91.11.y \(\chi_{91}(15, \cdot)\) 91.11.y.a 280 4
91.11.z \(\chi_{91}(18, \cdot)\) 91.11.z.a 368 4
91.11.bd \(\chi_{91}(11, \cdot)\) 91.11.bd.a 364 4

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(91))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(91)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 1}\)