## Defining parameters

 Level: $$N$$ = $$2166 = 2 \cdot 3 \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Sturm bound: $$519840$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2166))$$.

Total New Old
Modular forms 131976 32309 99667
Cusp forms 127945 32309 95636
Eisenstein series 4031 0 4031

## Trace form

 $$32309q - q^{2} - q^{3} - q^{4} - 6q^{5} - q^{6} - 8q^{7} - q^{8} - q^{9} + O(q^{10})$$ $$32309q - q^{2} - q^{3} - q^{4} - 6q^{5} - q^{6} - 8q^{7} - q^{8} - q^{9} - 6q^{10} - 12q^{11} + 11q^{12} + 82q^{13} + 64q^{14} + 66q^{15} - q^{16} + 54q^{17} - q^{18} + 84q^{19} + 66q^{20} + 76q^{21} + 96q^{22} + 48q^{23} - q^{24} + 113q^{25} + 58q^{26} + 29q^{27} + 16q^{28} + 42q^{29} - 6q^{30} + 40q^{31} - q^{32} + 96q^{33} - 18q^{34} + 96q^{35} - q^{36} + 34q^{37} + 94q^{39} - 6q^{40} + 30q^{41} - 8q^{42} + 100q^{43} - 12q^{44} - 6q^{45} - 24q^{46} + 24q^{47} - 19q^{48} + 15q^{49} - 31q^{50} - 180q^{51} - 14q^{52} - 54q^{53} - 109q^{54} - 72q^{55} - 8q^{56} - 90q^{57} - 30q^{58} - 60q^{59} - 78q^{60} - 38q^{61} - 32q^{62} - 140q^{63} - q^{64} - 12q^{65} - 156q^{66} + 76q^{67} - 18q^{68} - 132q^{69} - 48q^{70} - 19q^{72} + 34q^{73} - 38q^{74} + 53q^{75} + 48q^{77} + 58q^{78} + 232q^{79} - 6q^{80} + 143q^{81} + 102q^{82} + 204q^{83} + 100q^{84} + 180q^{85} + 100q^{86} + 330q^{87} - 12q^{88} + 198q^{89} + 174q^{90} + 272q^{91} + 120q^{92} + 268q^{93} + 240q^{94} + 108q^{95} - q^{96} + 118q^{97} + 231q^{98} + 150q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2166))$$

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
2166.2.a $$\chi_{2166}(1, \cdot)$$ 2166.2.a.a 1 1
2166.2.a.b 1
2166.2.a.c 1
2166.2.a.d 1
2166.2.a.e 1
2166.2.a.f 1
2166.2.a.g 1
2166.2.a.h 1
2166.2.a.i 1
2166.2.a.j 2
2166.2.a.k 2
2166.2.a.l 2
2166.2.a.m 2
2166.2.a.n 3
2166.2.a.o 3
2166.2.a.p 3
2166.2.a.q 3
2166.2.a.r 3
2166.2.a.s 3
2166.2.a.t 3
2166.2.a.u 3
2166.2.a.v 4
2166.2.a.w 4
2166.2.a.x 4
2166.2.a.y 4
2166.2.b $$\chi_{2166}(2165, \cdot)$$ n/a 112 1
2166.2.e $$\chi_{2166}(1375, \cdot)$$ n/a 116 2
2166.2.h $$\chi_{2166}(293, \cdot)$$ n/a 224 2
2166.2.i $$\chi_{2166}(415, \cdot)$$ n/a 336 6
2166.2.l $$\chi_{2166}(299, \cdot)$$ n/a 684 6
2166.2.m $$\chi_{2166}(115, \cdot)$$ n/a 1116 18
2166.2.p $$\chi_{2166}(113, \cdot)$$ n/a 2304 18
2166.2.q $$\chi_{2166}(7, \cdot)$$ n/a 2232 36
2166.2.r $$\chi_{2166}(65, \cdot)$$ n/a 4608 36
2166.2.u $$\chi_{2166}(25, \cdot)$$ n/a 6912 108
2166.2.v $$\chi_{2166}(29, \cdot)$$ n/a 13608 108

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2166))$$ into lower level spaces

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