# Properties

 Label 1666.2 Level 1666 Weight 2 Dimension 26894 Nonzero newspaces 20 Sturm bound 338688 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$1666 = 2 \cdot 7^{2} \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Sturm bound: $$338688$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1666))$$.

Total New Old
Modular forms 86592 26894 59698
Cusp forms 82753 26894 55859
Eisenstein series 3839 0 3839

## Trace form

 $$26894q - 2q^{2} + 6q^{4} + 12q^{5} + 16q^{6} + 16q^{7} - 2q^{8} + 30q^{9} + O(q^{10})$$ $$26894q - 2q^{2} + 6q^{4} + 12q^{5} + 16q^{6} + 16q^{7} - 2q^{8} + 30q^{9} + 16q^{10} + 40q^{11} + 8q^{12} + 28q^{13} + 12q^{14} + 96q^{15} + 10q^{16} + 46q^{17} + 54q^{18} + 64q^{19} + 16q^{20} + 52q^{21} + 40q^{22} + 64q^{23} + 24q^{24} + 78q^{25} + 48q^{26} + 120q^{27} + 16q^{28} + 56q^{29} + 48q^{30} + 80q^{31} - 2q^{32} + 128q^{33} + 6q^{34} + 84q^{35} + 30q^{36} + 4q^{37} - 44q^{38} + 12q^{39} - 72q^{40} + 8q^{41} - 108q^{42} + 8q^{43} - 28q^{44} - 180q^{45} - 172q^{46} - 40q^{47} - 28q^{48} - 236q^{49} - 30q^{50} - 56q^{51} + 16q^{52} + 32q^{53} - 132q^{54} - 196q^{55} - 72q^{56} + 64q^{57} - 52q^{58} + 8q^{59} - 4q^{60} + 8q^{61} + 44q^{62} + 72q^{63} + 6q^{64} + 204q^{65} + 104q^{66} + 136q^{67} + 34q^{68} + 256q^{69} + 84q^{70} + 192q^{71} + 42q^{72} + 240q^{73} + 104q^{74} + 400q^{75} + 48q^{76} + 168q^{77} + 144q^{78} + 272q^{79} + 28q^{80} + 134q^{81} + 128q^{82} + 48q^{83} + 52q^{84} + 156q^{85} + 88q^{86} + 96q^{87} + 56q^{88} + 84q^{89} + 224q^{90} + 20q^{91} + 64q^{92} - 88q^{93} + 208q^{94} + 48q^{95} + 16q^{96} + 84q^{97} + 96q^{98} - 224q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1666))$$

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
1666.2.a $$\chi_{1666}(1, \cdot)$$ 1666.2.a.a 1 1
1666.2.a.b 1
1666.2.a.c 1
1666.2.a.d 1
1666.2.a.e 1
1666.2.a.f 1
1666.2.a.g 1
1666.2.a.h 1
1666.2.a.i 1
1666.2.a.j 1
1666.2.a.k 1
1666.2.a.l 1
1666.2.a.m 1
1666.2.a.n 1
1666.2.a.o 2
1666.2.a.p 2
1666.2.a.q 2
1666.2.a.r 2
1666.2.a.s 2
1666.2.a.t 3
1666.2.a.u 3
1666.2.a.v 4
1666.2.a.w 4
1666.2.a.x 4
1666.2.a.y 4
1666.2.a.z 5
1666.2.a.ba 5
1666.2.b $$\chi_{1666}(883, \cdot)$$ 1666.2.b.a 2 1
1666.2.b.b 2
1666.2.b.c 2
1666.2.b.d 2
1666.2.b.e 2
1666.2.b.f 2
1666.2.b.g 4
1666.2.b.h 4
1666.2.b.i 4
1666.2.b.j 4
1666.2.b.k 6
1666.2.b.l 6
1666.2.b.m 6
1666.2.b.n 8
1666.2.b.o 8
1666.2.e $$\chi_{1666}(851, \cdot)$$ n/a 104 2
1666.2.g $$\chi_{1666}(1177, \cdot)$$ n/a 124 2
1666.2.j $$\chi_{1666}(67, \cdot)$$ n/a 120 2
1666.2.k $$\chi_{1666}(239, \cdot)$$ n/a 432 6
1666.2.l $$\chi_{1666}(393, \cdot)$$ n/a 244 4
1666.2.o $$\chi_{1666}(361, \cdot)$$ n/a 240 4
1666.2.r $$\chi_{1666}(169, \cdot)$$ n/a 504 6
1666.2.t $$\chi_{1666}(97, \cdot)$$ n/a 480 8
1666.2.u $$\chi_{1666}(137, \cdot)$$ n/a 912 12
1666.2.v $$\chi_{1666}(263, \cdot)$$ n/a 480 8
1666.2.x $$\chi_{1666}(183, \cdot)$$ n/a 1008 12
1666.2.z $$\chi_{1666}(135, \cdot)$$ n/a 1008 12
1666.2.bc $$\chi_{1666}(31, \cdot)$$ n/a 960 16
1666.2.bf $$\chi_{1666}(15, \cdot)$$ n/a 2016 24
1666.2.bg $$\chi_{1666}(81, \cdot)$$ n/a 2016 24
1666.2.bi $$\chi_{1666}(27, \cdot)$$ n/a 4032 48
1666.2.bl $$\chi_{1666}(9, \cdot)$$ n/a 4032 48
1666.2.bn $$\chi_{1666}(3, \cdot)$$ n/a 8064 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1666))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1666)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(119))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(238))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(833))$$$$^{\oplus 2}$$