# Properties

 Label 3762.2 Level 3762 Weight 2 Dimension 100328 Nonzero newspaces 64 Sturm bound 1555200 Trace bound 22

## Defining parameters

 Level: $$N$$ = $$3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$64$$ Sturm bound: $$1555200$$ Trace bound: $$22$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3762))$$.

Total New Old
Modular forms 394560 100328 294232
Cusp forms 383041 100328 282713
Eisenstein series 11519 0 11519

## Trace form

 $$100328 q - 4 q^{2} - 12 q^{3} - 4 q^{4} + 12 q^{6} - 28 q^{7} + 8 q^{8} + 12 q^{9} + O(q^{10})$$ $$100328 q - 4 q^{2} - 12 q^{3} - 4 q^{4} + 12 q^{6} - 28 q^{7} + 8 q^{8} + 12 q^{9} - 20 q^{10} - 14 q^{11} - 76 q^{13} - 64 q^{14} - 4 q^{16} - 100 q^{17} - 24 q^{18} - 103 q^{19} - 36 q^{20} + 24 q^{21} - 21 q^{22} + 28 q^{23} + 8 q^{24} + 28 q^{25} + 100 q^{26} + 120 q^{27} + 64 q^{28} + 100 q^{29} + 120 q^{30} + 80 q^{31} + 26 q^{32} + 182 q^{33} + 132 q^{34} + 208 q^{35} + 32 q^{36} + 52 q^{37} + 92 q^{38} + 120 q^{39} + 60 q^{40} + 88 q^{41} + 80 q^{42} + 28 q^{43} + 25 q^{44} + 256 q^{45} + 128 q^{46} + 232 q^{47} + 48 q^{48} + 108 q^{49} + 412 q^{50} + 416 q^{51} - 12 q^{52} + 588 q^{53} + 252 q^{54} + 236 q^{55} + 208 q^{56} + 446 q^{57} + 112 q^{58} + 678 q^{59} + 144 q^{60} + 408 q^{61} + 232 q^{62} + 400 q^{63} + 44 q^{64} + 624 q^{65} + 144 q^{66} + 300 q^{67} + 26 q^{68} + 376 q^{69} + 136 q^{70} + 352 q^{71} + 48 q^{72} + 110 q^{73} - 24 q^{74} + 80 q^{75} - 8 q^{76} + 136 q^{77} - 24 q^{78} - 80 q^{79} - 20 q^{80} - 116 q^{81} + 50 q^{82} - 402 q^{83} - 184 q^{84} - 204 q^{85} - 338 q^{86} - 328 q^{87} - 14 q^{88} - 456 q^{89} - 400 q^{90} + 120 q^{91} - 228 q^{92} - 400 q^{93} - 80 q^{94} - 162 q^{95} + 58 q^{97} - 438 q^{98} - 478 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3762))$$

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
3762.2.a $$\chi_{3762}(1, \cdot)$$ 3762.2.a.a 1 1
3762.2.a.b 1
3762.2.a.c 1
3762.2.a.d 1
3762.2.a.e 1
3762.2.a.f 1
3762.2.a.g 1
3762.2.a.h 1
3762.2.a.i 1
3762.2.a.j 1
3762.2.a.k 1
3762.2.a.l 1
3762.2.a.m 1
3762.2.a.n 1
3762.2.a.o 1
3762.2.a.p 1
3762.2.a.q 1
3762.2.a.r 1
3762.2.a.s 2
3762.2.a.t 2
3762.2.a.u 2
3762.2.a.v 2
3762.2.a.w 2
3762.2.a.x 2
3762.2.a.y 2
3762.2.a.z 2
3762.2.a.ba 2
3762.2.a.bb 2
3762.2.a.bc 2
3762.2.a.bd 3
3762.2.a.be 3
3762.2.a.bf 3
3762.2.a.bg 3
3762.2.a.bh 4
3762.2.a.bi 5
3762.2.a.bj 5
3762.2.a.bk 5
3762.2.a.bl 5
3762.2.b $$\chi_{3762}(989, \cdot)$$ 3762.2.b.a 36 1
3762.2.b.b 36
3762.2.d $$\chi_{3762}(683, \cdot)$$ 3762.2.d.a 36 1
3762.2.d.b 36
3762.2.g $$\chi_{3762}(2089, \cdot)$$ 3762.2.g.a 2 1
3762.2.g.b 2
3762.2.g.c 2
3762.2.g.d 2
3762.2.g.e 2
3762.2.g.f 2
3762.2.g.g 8
3762.2.g.h 8
3762.2.g.i 16
3762.2.g.j 16
3762.2.g.k 20
3762.2.g.l 20
3762.2.i $$\chi_{3762}(1255, \cdot)$$ n/a 360 2
3762.2.j $$\chi_{3762}(1717, \cdot)$$ n/a 400 2
3762.2.k $$\chi_{3762}(1189, \cdot)$$ n/a 172 2
3762.2.l $$\chi_{3762}(463, \cdot)$$ n/a 400 2
3762.2.m $$\chi_{3762}(685, \cdot)$$ n/a 360 4
3762.2.o $$\chi_{3762}(221, \cdot)$$ n/a 400 2
3762.2.q $$\chi_{3762}(2705, \cdot)$$ n/a 480 2
3762.2.r $$\chi_{3762}(901, \cdot)$$ n/a 200 2
3762.2.w $$\chi_{3762}(835, \cdot)$$ n/a 480 2
3762.2.y $$\chi_{3762}(1627, \cdot)$$ n/a 480 2
3762.2.bb $$\chi_{3762}(197, \cdot)$$ n/a 160 2
3762.2.bc $$\chi_{3762}(2003, \cdot)$$ n/a 400 2
3762.2.be $$\chi_{3762}(1937, \cdot)$$ n/a 400 2
3762.2.bg $$\chi_{3762}(923, \cdot)$$ n/a 480 2
3762.2.bi $$\chi_{3762}(2243, \cdot)$$ n/a 432 2
3762.2.bl $$\chi_{3762}(1475, \cdot)$$ n/a 144 2
3762.2.bn $$\chi_{3762}(373, \cdot)$$ n/a 480 2
3762.2.bp $$\chi_{3762}(199, \cdot)$$ n/a 492 6
3762.2.bq $$\chi_{3762}(1651, \cdot)$$ n/a 1200 6
3762.2.br $$\chi_{3762}(529, \cdot)$$ n/a 1200 6
3762.2.bt $$\chi_{3762}(721, \cdot)$$ n/a 400 4
3762.2.bw $$\chi_{3762}(1367, \cdot)$$ n/a 320 4
3762.2.by $$\chi_{3762}(305, \cdot)$$ n/a 288 4
3762.2.bz $$\chi_{3762}(619, \cdot)$$ n/a 1920 8
3762.2.ca $$\chi_{3762}(163, \cdot)$$ n/a 800 8
3762.2.cb $$\chi_{3762}(49, \cdot)$$ n/a 1920 8
3762.2.cc $$\chi_{3762}(115, \cdot)$$ n/a 1728 8
3762.2.cd $$\chi_{3762}(263, \cdot)$$ n/a 1440 6
3762.2.cf $$\chi_{3762}(439, \cdot)$$ n/a 1440 6
3762.2.ci $$\chi_{3762}(1211, \cdot)$$ n/a 1200 6
3762.2.ck $$\chi_{3762}(89, \cdot)$$ n/a 384 6
3762.2.co $$\chi_{3762}(241, \cdot)$$ n/a 1440 6
3762.2.cp $$\chi_{3762}(593, \cdot)$$ n/a 480 6
3762.2.cr $$\chi_{3762}(109, \cdot)$$ n/a 600 6
3762.2.cu $$\chi_{3762}(131, \cdot)$$ n/a 1440 6
3762.2.cw $$\chi_{3762}(155, \cdot)$$ n/a 1200 6
3762.2.cz $$\chi_{3762}(673, \cdot)$$ n/a 1920 8
3762.2.db $$\chi_{3762}(179, \cdot)$$ n/a 640 8
3762.2.de $$\chi_{3762}(761, \cdot)$$ n/a 1728 8
3762.2.dg $$\chi_{3762}(83, \cdot)$$ n/a 1920 8
3762.2.di $$\chi_{3762}(113, \cdot)$$ n/a 1920 8
3762.2.dk $$\chi_{3762}(335, \cdot)$$ n/a 1920 8
3762.2.dl $$\chi_{3762}(809, \cdot)$$ n/a 640 8
3762.2.do $$\chi_{3762}(259, \cdot)$$ n/a 1920 8
3762.2.dq $$\chi_{3762}(151, \cdot)$$ n/a 1920 8
3762.2.dv $$\chi_{3762}(145, \cdot)$$ n/a 800 8
3762.2.dw $$\chi_{3762}(695, \cdot)$$ n/a 1920 8
3762.2.dy $$\chi_{3762}(905, \cdot)$$ n/a 1920 8
3762.2.ea $$\chi_{3762}(169, \cdot)$$ n/a 5760 24
3762.2.eb $$\chi_{3762}(25, \cdot)$$ n/a 5760 24
3762.2.ec $$\chi_{3762}(289, \cdot)$$ n/a 2400 24
3762.2.ed $$\chi_{3762}(203, \cdot)$$ n/a 5760 24
3762.2.eh $$\chi_{3762}(101, \cdot)$$ n/a 5760 24
3762.2.ei $$\chi_{3762}(127, \cdot)$$ n/a 2400 24
3762.2.ek $$\chi_{3762}(17, \cdot)$$ n/a 1920 24
3762.2.en $$\chi_{3762}(193, \cdot)$$ n/a 5760 24
3762.2.ep $$\chi_{3762}(53, \cdot)$$ n/a 1920 24
3762.2.et $$\chi_{3762}(59, \cdot)$$ n/a 5760 24
3762.2.eu $$\chi_{3762}(13, \cdot)$$ n/a 5760 24
3762.2.ew $$\chi_{3762}(365, \cdot)$$ n/a 5760 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3762))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3762)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(198))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(209))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(342))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(418))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(627))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1254))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1881))$$$$^{\oplus 2}$$