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

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

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

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