↑

Properties

Label 91.3
Level 91
Weight 3
Dimension 582
Nonzero newspaces 15
Newform subspaces 20
Sturm bound 2016
Trace bound 5

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 91 = 7 \cdot 13 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 20 \)
Sturm bound: \(2016\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(91))\).

Total New Old
Modular forms 744 690 54
Cusp forms 600 582 18
Eisenstein series 144 108 36

Trace form

\( 582 q - 18 q^{2} - 24 q^{3} - 34 q^{4} - 24 q^{5} - 24 q^{6} - 26 q^{7} - 126 q^{8} - 90 q^{9} + O(q^{10}) \) \( 582 q - 18 q^{2} - 24 q^{3} - 34 q^{4} - 24 q^{5} - 24 q^{6} - 26 q^{7} - 126 q^{8} - 90 q^{9} - 84 q^{10} - 24 q^{11} - 36 q^{12} - 78 q^{14} + 12 q^{15} + 158 q^{16} - 12 q^{17} - 42 q^{18} - 56 q^{19} - 120 q^{20} - 108 q^{21} - 276 q^{22} - 108 q^{23} - 168 q^{24} - 86 q^{25} + 36 q^{26} + 96 q^{27} + 74 q^{28} - 48 q^{29} + 72 q^{30} - 76 q^{31} - 126 q^{32} + 180 q^{33} + 216 q^{34} - 54 q^{36} + 96 q^{37} - 36 q^{38} - 168 q^{39} - 384 q^{40} - 300 q^{41} - 156 q^{42} - 548 q^{43} + 192 q^{44} - 144 q^{45} - 132 q^{46} + 108 q^{47} + 216 q^{48} - 62 q^{49} + 426 q^{50} - 36 q^{51} - 196 q^{52} - 156 q^{53} - 372 q^{54} + 36 q^{55} + 6 q^{56} + 48 q^{57} + 180 q^{59} + 180 q^{60} + 804 q^{61} - 48 q^{62} + 102 q^{63} + 110 q^{64} - 252 q^{65} - 456 q^{66} + 132 q^{67} - 1068 q^{68} - 180 q^{69} - 168 q^{70} - 696 q^{71} + 1266 q^{72} + 52 q^{73} + 552 q^{74} + 1128 q^{75} + 2464 q^{76} + 1284 q^{77} + 2328 q^{78} + 1652 q^{79} + 3300 q^{80} + 1650 q^{81} + 2220 q^{82} + 1200 q^{83} + 2160 q^{84} + 1104 q^{85} + 1296 q^{86} + 216 q^{87} + 1200 q^{88} - 72 q^{89} - 400 q^{91} + 324 q^{92} - 624 q^{93} - 624 q^{94} - 600 q^{95} - 3348 q^{96} - 1768 q^{97} - 1398 q^{98} - 2628 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(91))\)

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
91.3.b \(\chi_{91}(90, \cdot)\) 91.3.b.a 1 1
91.3.b.b 1
91.3.b.c 4
91.3.b.d 6
91.3.b.e 6
91.3.d \(\chi_{91}(27, \cdot)\) 91.3.d.a 16 1
91.3.j \(\chi_{91}(8, \cdot)\) 91.3.j.a 28 2
91.3.l \(\chi_{91}(17, \cdot)\) 91.3.l.a 34 2
91.3.m \(\chi_{91}(3, \cdot)\) 91.3.m.a 34 2
91.3.n \(\chi_{91}(48, \cdot)\) 91.3.n.a 4 2
91.3.n.b 28
91.3.o \(\chi_{91}(40, \cdot)\) 91.3.o.a 32 2
91.3.p \(\chi_{91}(10, \cdot)\) 91.3.p.a 34 2
91.3.s \(\chi_{91}(12, \cdot)\) 91.3.s.a 32 2
91.3.t \(\chi_{91}(62, \cdot)\) 91.3.t.a 32 2
91.3.v \(\chi_{91}(68, \cdot)\) 91.3.v.a 34 2
91.3.x \(\chi_{91}(2, \cdot)\) 91.3.x.a 68 4
91.3.y \(\chi_{91}(15, \cdot)\) 91.3.y.a 56 4
91.3.z \(\chi_{91}(18, \cdot)\) 91.3.z.a 64 4
91.3.bd \(\chi_{91}(11, \cdot)\) 91.3.bd.a 68 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(91))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(91)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 1}\)