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Properties

Label 91.8
Level 91
Weight 8
Dimension 2172
Nonzero newspaces 15
Newform subspaces 21
Sturm bound 5376
Trace bound 3

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Defining parameters

Level: \( N \) = \( 91 = 7 \cdot 13 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 21 \)
Sturm bound: \(5376\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(91))\).

Total New Old
Modular forms 2424 2284 140
Cusp forms 2280 2172 108
Eisenstein series 144 112 32

Trace form

\( 2172 q - 18 q^{2} - 72 q^{3} + 494 q^{4} - 12 q^{5} - 2604 q^{6} + 826 q^{7} - 5610 q^{8} + 12954 q^{9} + O(q^{10}) \) \( 2172 q - 18 q^{2} - 72 q^{3} + 494 q^{4} - 12 q^{5} - 2604 q^{6} + 826 q^{7} - 5610 q^{8} + 12954 q^{9} + 38076 q^{10} - 10428 q^{11} - 109872 q^{12} - 24982 q^{13} - 82158 q^{14} + 93084 q^{15} + 341958 q^{16} + 275178 q^{17} - 408546 q^{18} - 399952 q^{19} - 538056 q^{20} + 58404 q^{21} + 891552 q^{22} + 429240 q^{23} - 60876 q^{24} - 345556 q^{25} - 1113888 q^{26} - 1364616 q^{27} - 494306 q^{28} - 414702 q^{29} + 3270060 q^{30} + 1801508 q^{31} + 1306422 q^{32} - 559356 q^{33} - 1620612 q^{34} - 196464 q^{35} - 88422 q^{36} + 25610 q^{37} - 3866508 q^{38} + 1530312 q^{39} - 6152592 q^{40} - 6437118 q^{41} - 1000380 q^{42} + 4102296 q^{43} + 9310476 q^{44} + 9316710 q^{45} + 14410644 q^{46} + 7197780 q^{47} + 1973964 q^{48} - 589218 q^{49} - 19043058 q^{50} - 15450756 q^{51} - 17807976 q^{52} - 18278268 q^{53} - 12351720 q^{54} + 18037884 q^{55} + 23261658 q^{56} + 18879624 q^{57} + 20094036 q^{58} + 11441484 q^{59} + 19186260 q^{60} + 5163466 q^{61} + 14435544 q^{62} - 10612782 q^{63} - 79301506 q^{64} - 52052502 q^{65} - 38322516 q^{66} + 15906536 q^{67} + 42380880 q^{68} + 13910244 q^{69} + 11581620 q^{70} + 38308812 q^{71} + 88984710 q^{72} + 3763040 q^{73} - 9032112 q^{74} - 6629760 q^{75} + 13095452 q^{76} + 38664768 q^{77} - 108878688 q^{78} - 11427392 q^{79} - 80690580 q^{80} - 50523330 q^{81} - 130393164 q^{82} - 53260080 q^{83} - 136390836 q^{84} + 52040466 q^{85} + 165261804 q^{86} + 90581664 q^{87} + 122261652 q^{88} - 11365644 q^{89} + 30678432 q^{90} + 71169658 q^{91} + 53056440 q^{92} + 127405968 q^{93} + 99927660 q^{94} + 129800664 q^{95} + 102506592 q^{96} - 71943676 q^{97} - 220068606 q^{98} - 278491440 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(91))\)

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
91.8.a \(\chi_{91}(1, \cdot)\) 91.8.a.a 1 1
91.8.a.b 9
91.8.a.c 10
91.8.a.d 10
91.8.a.e 12
91.8.c \(\chi_{91}(64, \cdot)\) 91.8.c.a 50 1
91.8.e \(\chi_{91}(53, \cdot)\) 91.8.e.a 54 2
91.8.e.b 58
91.8.f \(\chi_{91}(22, \cdot)\) 91.8.f.a 48 2
91.8.f.b 48
91.8.g \(\chi_{91}(9, \cdot)\) 91.8.g.a 126 2
91.8.h \(\chi_{91}(16, \cdot)\) 91.8.h.a 126 2
91.8.i \(\chi_{91}(34, \cdot)\) 91.8.i.a 124 2
91.8.k \(\chi_{91}(4, \cdot)\) 91.8.k.a 126 2
91.8.q \(\chi_{91}(36, \cdot)\) 91.8.q.a 100 2
91.8.r \(\chi_{91}(25, \cdot)\) 91.8.r.a 128 2
91.8.u \(\chi_{91}(30, \cdot)\) 91.8.u.a 126 2
91.8.w \(\chi_{91}(19, \cdot)\) 91.8.w.a 252 4
91.8.ba \(\chi_{91}(45, \cdot)\) 91.8.ba.a 252 4
91.8.bb \(\chi_{91}(5, \cdot)\) 91.8.bb.a 256 4
91.8.bc \(\chi_{91}(6, \cdot)\) 91.8.bc.a 256 4

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(91))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(91)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)