Properties

Label 91.10
Level 91
Weight 10
Dimension 2808
Nonzero newspaces 15
Newform subspaces 20
Sturm bound 6720
Trace bound 3

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Defining parameters

Level: \( N \) = \( 91 = 7 \cdot 13 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 20 \)
Sturm bound: \(6720\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(91))\).

Total New Old
Modular forms 3096 2920 176
Cusp forms 2952 2808 144
Eisenstein series 144 112 32

Trace form

\( 2808 q - 18 q^{2} - 342 q^{3} - 18 q^{4} - 1722 q^{5} + 15540 q^{6} - 708 q^{7} - 28218 q^{8} + 101370 q^{9} + O(q^{10}) \) \( 2808 q - 18 q^{2} - 342 q^{3} - 18 q^{4} - 1722 q^{5} + 15540 q^{6} - 708 q^{7} - 28218 q^{8} + 101370 q^{9} - 206388 q^{10} - 111354 q^{11} + 666720 q^{12} + 582828 q^{13} - 414510 q^{14} - 1282800 q^{15} - 1608570 q^{16} + 1060464 q^{17} - 83970 q^{18} + 3329262 q^{19} + 3502872 q^{20} + 1207344 q^{21} - 11038896 q^{22} - 12763518 q^{23} - 1203804 q^{24} + 4017036 q^{25} + 26203704 q^{26} + 34477884 q^{27} + 19619358 q^{28} - 67483962 q^{29} - 76611204 q^{30} - 5774346 q^{31} + 64384038 q^{32} + 102530010 q^{33} + 61909116 q^{34} + 6537984 q^{35} - 130471926 q^{36} - 36378264 q^{37} - 78569820 q^{38} + 166230078 q^{39} + 5901696 q^{40} + 60427806 q^{41} + 338038692 q^{42} + 71810220 q^{43} - 469801428 q^{44} - 421301394 q^{45} - 515709804 q^{46} + 132436290 q^{47} + 508173132 q^{48} + 75250272 q^{49} + 280535550 q^{50} - 12814746 q^{51} + 521075688 q^{52} + 255183330 q^{53} + 520671336 q^{54} + 8354844 q^{55} - 697089270 q^{56} - 968499000 q^{57} - 797101308 q^{58} - 302992038 q^{59} + 63652452 q^{60} + 1318571544 q^{61} + 1066892664 q^{62} - 558983880 q^{63} - 1028445474 q^{64} + 130270704 q^{65} + 4566231420 q^{66} + 3732977886 q^{67} - 1210263024 q^{68} - 4972047852 q^{69} - 3021521244 q^{70} - 1722395820 q^{71} - 1787568282 q^{72} - 893412198 q^{73} + 2632434624 q^{74} + 6075201456 q^{75} + 5746655196 q^{76} - 3229426590 q^{77} + 472830192 q^{78} - 3159886734 q^{79} - 3665026836 q^{80} - 1288631820 q^{81} + 3681019764 q^{82} - 985784820 q^{83} + 10504984524 q^{84} + 7817067474 q^{85} + 1000646268 q^{86} - 4629536412 q^{87} - 6461236908 q^{88} - 2950876902 q^{89} + 781658592 q^{90} - 3485445750 q^{91} - 4919981832 q^{92} - 7684184046 q^{93} - 10792163268 q^{94} - 2259861570 q^{95} + 21953465760 q^{96} + 13691346348 q^{97} + 7665523602 q^{98} + 884374836 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(91))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
91.10.a \(\chi_{91}(1, \cdot)\) 91.10.a.a 12 1
91.10.a.b 13
91.10.a.c 14
91.10.a.d 15
91.10.c \(\chi_{91}(64, \cdot)\) 91.10.c.a 62 1
91.10.e \(\chi_{91}(53, \cdot)\) 91.10.e.a 70 2
91.10.e.b 74
91.10.f \(\chi_{91}(22, \cdot)\) 91.10.f.a 64 2
91.10.f.b 64
91.10.g \(\chi_{91}(9, \cdot)\) 91.10.g.a 164 2
91.10.h \(\chi_{91}(16, \cdot)\) 91.10.h.a 164 2
91.10.i \(\chi_{91}(34, \cdot)\) 91.10.i.a 164 2
91.10.k \(\chi_{91}(4, \cdot)\) 91.10.k.a 164 2
91.10.q \(\chi_{91}(36, \cdot)\) 91.10.q.a 124 2
91.10.r \(\chi_{91}(25, \cdot)\) 91.10.r.a 164 2
91.10.u \(\chi_{91}(30, \cdot)\) 91.10.u.a 164 2
91.10.w \(\chi_{91}(19, \cdot)\) 91.10.w.a 328 4
91.10.ba \(\chi_{91}(45, \cdot)\) 91.10.ba.a 328 4
91.10.bb \(\chi_{91}(5, \cdot)\) 91.10.bb.a 328 4
91.10.bc \(\chi_{91}(6, \cdot)\) 91.10.bc.a 328 4

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(91))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(91)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)