Properties

Label 2166.4
Level 2166
Weight 4
Dimension 96931
Nonzero newspaces 12
Sturm bound 1039680
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(1039680\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2166))\).

Total New Old
Modular forms 391896 96931 294965
Cusp forms 387864 96931 290933
Eisenstein series 4032 0 4032

Trace form

\( 96931q - 2q^{2} - 3q^{3} + 4q^{4} + 6q^{5} + 6q^{6} - 16q^{7} - 8q^{8} + 9q^{9} + O(q^{10}) \) \( 96931q - 2q^{2} - 3q^{3} + 4q^{4} + 6q^{5} + 6q^{6} - 16q^{7} - 8q^{8} + 9q^{9} - 12q^{10} + 12q^{11} + 276q^{12} + 1190q^{13} + 176q^{14} - 450q^{15} + 16q^{16} - 1278q^{17} - 18q^{18} - 1512q^{19} - 1128q^{20} - 960q^{21} - 672q^{22} + 312q^{23} + 24q^{24} + 3367q^{25} + 2660q^{26} + 1935q^{27} + 1664q^{28} + 2550q^{29} + 36q^{30} + 272q^{31} - 32q^{32} - 1872q^{33} + 252q^{34} - 4560q^{35} + 36q^{36} - 2410q^{37} - 3894q^{39} - 48q^{40} - 1758q^{41} - 96q^{42} - 1060q^{43} + 48q^{44} - 6102q^{45} - 336q^{46} + 3720q^{47} - 336q^{48} + 6753q^{49} + 178q^{50} + 7668q^{51} + 152q^{52} + 198q^{53} + 5454q^{54} + 72q^{55} + 128q^{56} + 5040q^{57} - 60q^{58} - 660q^{59} + 3096q^{60} + 2702q^{61} + 176q^{62} + 2844q^{63} + 64q^{64} + 2748q^{65} - 4824q^{66} + 452q^{67} - 504q^{68} - 11304q^{69} + 192q^{70} - 3168q^{71} - 3384q^{72} - 7234q^{73} - 508q^{74} - 6033q^{75} + 9816q^{77} + 13044q^{78} + 9920q^{79} + 96q^{80} + 12753q^{81} + 8844q^{82} + 6348q^{83} + 1920q^{84} - 1908q^{85} - 3064q^{86} - 6930q^{87} - 96q^{88} - 5310q^{89} - 13428q^{90} - 8384q^{91} - 12000q^{92} - 23460q^{93} - 26880q^{94} - 10152q^{95} + 96q^{96} - 17854q^{97} - 23442q^{98} - 33426q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2166))\)

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
2166.4.a \(\chi_{2166}(1, \cdot)\) 2166.4.a.a 1 1
2166.4.a.b 1
2166.4.a.c 1
2166.4.a.d 1
2166.4.a.e 1
2166.4.a.f 1
2166.4.a.g 1
2166.4.a.h 1
2166.4.a.i 1
2166.4.a.j 2
2166.4.a.k 2
2166.4.a.l 2
2166.4.a.m 2
2166.4.a.n 2
2166.4.a.o 2
2166.4.a.p 2
2166.4.a.q 2
2166.4.a.r 3
2166.4.a.s 3
2166.4.a.t 3
2166.4.a.u 3
2166.4.a.v 3
2166.4.a.w 3
2166.4.a.x 4
2166.4.a.y 4
2166.4.a.z 4
2166.4.a.ba 4
2166.4.a.bb 6
2166.4.a.bc 6
2166.4.a.bd 6
2166.4.a.be 6
2166.4.a.bf 6
2166.4.a.bg 6
2166.4.a.bh 8
2166.4.a.bi 8
2166.4.a.bj 9
2166.4.a.bk 9
2166.4.a.bl 9
2166.4.a.bm 9
2166.4.a.bn 12
2166.4.a.bo 12
2166.4.b \(\chi_{2166}(2165, \cdot)\) n/a 340 1
2166.4.e \(\chi_{2166}(1375, \cdot)\) n/a 340 2
2166.4.h \(\chi_{2166}(293, \cdot)\) n/a 680 2
2166.4.i \(\chi_{2166}(415, \cdot)\) n/a 1020 6
2166.4.l \(\chi_{2166}(299, \cdot)\) n/a 2040 6
2166.4.m \(\chi_{2166}(115, \cdot)\) n/a 3420 18
2166.4.p \(\chi_{2166}(113, \cdot)\) n/a 6840 18
2166.4.q \(\chi_{2166}(7, \cdot)\) n/a 6840 36
2166.4.r \(\chi_{2166}(65, \cdot)\) n/a 13680 36
2166.4.u \(\chi_{2166}(25, \cdot)\) n/a 20520 108
2166.4.v \(\chi_{2166}(29, \cdot)\) n/a 41040 108

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2166))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2166)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 2}\)