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Properties

Label 91.7
Level 91
Weight 7
Dimension 1854
Nonzero newspaces 15
Newform subspaces 17
Sturm bound 4704
Trace bound 4

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Defining parameters

Level: \( N \) = \( 91 = 7 \cdot 13 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 17 \)
Sturm bound: \(4704\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(91))\).

Total New Old
Modular forms 2088 1962 126
Cusp forms 1944 1854 90
Eisenstein series 144 108 36

Trace form

\( 1854 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 354 q^{5} - 24 q^{6} + 216 q^{7} + 5970 q^{8} + 3678 q^{9} + O(q^{10}) \) \( 1854 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 354 q^{5} - 24 q^{6} + 216 q^{7} + 5970 q^{8} + 3678 q^{9} - 14544 q^{10} - 12090 q^{11} - 11964 q^{12} + 10920 q^{13} + 31362 q^{14} + 49152 q^{15} + 20022 q^{16} - 58290 q^{17} - 87702 q^{18} - 35466 q^{19} + 67320 q^{20} + 71904 q^{21} - 13620 q^{22} - 49554 q^{23} - 215304 q^{24} - 125526 q^{25} + 81708 q^{26} + 254976 q^{27} + 84114 q^{28} + 229128 q^{29} + 581832 q^{30} + 192966 q^{31} - 119814 q^{32} - 449802 q^{33} - 723624 q^{34} - 413400 q^{35} - 585966 q^{36} - 106482 q^{37} - 121956 q^{38} - 149388 q^{39} + 1033536 q^{40} + 1095228 q^{41} + 572532 q^{42} + 517680 q^{43} + 795240 q^{44} + 115416 q^{45} - 1005300 q^{46} - 589338 q^{47} - 3212856 q^{48} - 1511688 q^{49} - 2682474 q^{50} - 1206774 q^{51} + 2571516 q^{52} + 1650654 q^{53} + 4373916 q^{54} + 2939016 q^{55} + 1327470 q^{56} + 1933008 q^{57} + 534372 q^{58} - 274626 q^{59} - 6173460 q^{60} - 3847182 q^{61} - 7483968 q^{62} - 1766328 q^{63} + 187926 q^{64} + 3943608 q^{65} + 8939424 q^{66} + 2588862 q^{67} + 4165140 q^{68} + 2951496 q^{69} + 3393792 q^{70} + 815712 q^{71} - 1461990 q^{72} - 1901466 q^{73} - 4286028 q^{74} - 8584152 q^{75} - 13860240 q^{76} - 9427422 q^{77} - 7602888 q^{78} - 4964538 q^{79} + 2427300 q^{80} + 5844252 q^{81} + 9458688 q^{82} + 10635096 q^{83} + 25134288 q^{84} + 12105204 q^{85} + 7792176 q^{86} + 11275020 q^{87} + 10896816 q^{88} + 10041606 q^{89} - 1272918 q^{91} - 19424700 q^{92} - 15654666 q^{93} - 20952144 q^{94} - 10076610 q^{95} - 34970868 q^{96} - 24046632 q^{97} - 22589262 q^{98} - 24056928 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(91))\)

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
91.7.b \(\chi_{91}(90, \cdot)\) 91.7.b.a 1 1
91.7.b.b 1
91.7.b.c 52
91.7.d \(\chi_{91}(27, \cdot)\) 91.7.d.a 48 1
91.7.j \(\chi_{91}(8, \cdot)\) 91.7.j.a 84 2
91.7.l \(\chi_{91}(17, \cdot)\) 91.7.l.a 108 2
91.7.m \(\chi_{91}(3, \cdot)\) 91.7.m.a 108 2
91.7.n \(\chi_{91}(48, \cdot)\) 91.7.n.a 108 2
91.7.o \(\chi_{91}(40, \cdot)\) 91.7.o.a 96 2
91.7.p \(\chi_{91}(10, \cdot)\) 91.7.p.a 108 2
91.7.s \(\chi_{91}(12, \cdot)\) 91.7.s.a 108 2
91.7.t \(\chi_{91}(62, \cdot)\) 91.7.t.a 108 2
91.7.v \(\chi_{91}(68, \cdot)\) 91.7.v.a 108 2
91.7.x \(\chi_{91}(2, \cdot)\) 91.7.x.a 216 4
91.7.y \(\chi_{91}(15, \cdot)\) 91.7.y.a 168 4
91.7.z \(\chi_{91}(18, \cdot)\) 91.7.z.a 216 4
91.7.bd \(\chi_{91}(11, \cdot)\) 91.7.bd.a 216 4

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(91))\) into lower level spaces

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