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Properties

Label 91.5
Level 91
Weight 5
Dimension 1218
Nonzero newspaces 15
Newform subspaces 17
Sturm bound 3360
Trace bound 3

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Defining parameters

Level: \( N \) = \( 91 = 7 \cdot 13 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 17 \)
Sturm bound: \(3360\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(91))\).

Total New Old
Modular forms 1416 1326 90
Cusp forms 1272 1218 54
Eisenstein series 144 108 36

Trace form

\( 1218 q - 18 q^{2} - 36 q^{3} + 46 q^{4} + 36 q^{5} - 24 q^{6} - 238 q^{7} - 606 q^{8} + 294 q^{9} + O(q^{10}) \) \( 1218 q - 18 q^{2} - 36 q^{3} + 46 q^{4} + 36 q^{5} - 24 q^{6} - 238 q^{7} - 606 q^{8} + 294 q^{9} + 1344 q^{10} + 756 q^{11} + 1140 q^{12} - 624 q^{13} - 1854 q^{14} - 2508 q^{15} - 2858 q^{16} - 1512 q^{17} - 3894 q^{18} + 212 q^{19} + 7032 q^{20} + 5268 q^{21} + 9180 q^{22} + 2880 q^{23} + 2856 q^{24} - 142 q^{25} - 4092 q^{26} - 7248 q^{27} - 6158 q^{28} - 8184 q^{29} - 18216 q^{30} - 8456 q^{31} + 1194 q^{32} + 2448 q^{33} + 15576 q^{34} + 14016 q^{35} + 37122 q^{36} + 10188 q^{37} + 12300 q^{38} - 14964 q^{39} - 32784 q^{40} - 18096 q^{41} - 20460 q^{42} - 1612 q^{43} - 24600 q^{44} + 8028 q^{45} + 26124 q^{46} + 13824 q^{47} + 24840 q^{48} + 8942 q^{49} + 11334 q^{50} + 9432 q^{51} - 7508 q^{52} + 1488 q^{53} - 4116 q^{54} - 26724 q^{55} - 2658 q^{56} - 36048 q^{57} - 19788 q^{58} - 9072 q^{59} + 11772 q^{60} - 11124 q^{61} - 39264 q^{62} - 18654 q^{63} + 16150 q^{64} + 14700 q^{65} + 61968 q^{66} + 22272 q^{67} - 6828 q^{68} - 4860 q^{69} + 20400 q^{70} + 60360 q^{71} + 39354 q^{72} + 37856 q^{73} + 121572 q^{74} + 97176 q^{75} + 89840 q^{76} + 58992 q^{77} + 168 q^{78} - 6272 q^{79} - 147516 q^{80} - 110850 q^{81} - 211680 q^{82} - 152592 q^{83} - 299568 q^{84} - 204780 q^{85} - 308352 q^{86} - 248760 q^{87} - 237264 q^{88} - 132516 q^{89} + 32452 q^{91} + 211140 q^{92} + 244788 q^{93} + 325632 q^{94} + 302796 q^{95} + 552204 q^{96} + 163624 q^{97} + 188418 q^{98} + 248292 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(91))\)

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
91.5.b \(\chi_{91}(90, \cdot)\) 91.5.b.a 1 1
91.5.b.b 1
91.5.b.c 32
91.5.d \(\chi_{91}(27, \cdot)\) 91.5.d.a 32 1
91.5.j \(\chi_{91}(8, \cdot)\) 91.5.j.a 56 2
91.5.l \(\chi_{91}(17, \cdot)\) 91.5.l.a 70 2
91.5.m \(\chi_{91}(3, \cdot)\) 91.5.m.a 70 2
91.5.n \(\chi_{91}(48, \cdot)\) 91.5.n.a 72 2
91.5.o \(\chi_{91}(40, \cdot)\) 91.5.o.a 64 2
91.5.p \(\chi_{91}(10, \cdot)\) 91.5.p.a 70 2
91.5.s \(\chi_{91}(12, \cdot)\) 91.5.s.a 72 2
91.5.t \(\chi_{91}(62, \cdot)\) 91.5.t.a 72 2
91.5.v \(\chi_{91}(68, \cdot)\) 91.5.v.a 70 2
91.5.x \(\chi_{91}(2, \cdot)\) 91.5.x.a 140 4
91.5.y \(\chi_{91}(15, \cdot)\) 91.5.y.a 112 4
91.5.z \(\chi_{91}(18, \cdot)\) 91.5.z.a 144 4
91.5.bd \(\chi_{91}(11, \cdot)\) 91.5.bd.a 140 4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(91))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(91)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 1}\)