## Defining parameters

 Level: $$N$$ = $$1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$138240$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1140))$$.

Total New Old
Modular forms 36000 13992 22008
Cusp forms 33121 13576 19545
Eisenstein series 2879 416 2463

## Trace form

 $$13576q - 4q^{3} - 20q^{4} - 4q^{5} - 38q^{6} + 8q^{7} + 24q^{8} - 16q^{9} + O(q^{10})$$ $$13576q - 4q^{3} - 20q^{4} - 4q^{5} - 38q^{6} + 8q^{7} + 24q^{8} - 16q^{9} - 14q^{10} + 16q^{11} - 10q^{12} - 72q^{13} + 10q^{15} - 108q^{16} + 4q^{17} - 32q^{18} - 84q^{19} - 40q^{20} - 126q^{21} - 52q^{22} - 36q^{23} - 66q^{24} - 116q^{25} - 32q^{26} - 16q^{27} + 24q^{28} + 48q^{29} - 36q^{30} + 24q^{31} + 140q^{32} + 48q^{33} + 96q^{34} + 40q^{35} + 126q^{36} + 72q^{37} + 236q^{38} + 108q^{39} + 40q^{40} + 80q^{41} + 146q^{42} + 168q^{43} + 180q^{44} + 31q^{45} + 120q^{46} + 72q^{47} + 148q^{48} + 36q^{49} + 86q^{50} + 132q^{51} + 44q^{52} - 8q^{53} + 94q^{54} + 16q^{55} + 128q^{56} + 34q^{57} + 40q^{58} + 16q^{59} + 110q^{60} + 24q^{61} - 68q^{62} + 68q^{63} - 212q^{64} + 68q^{65} - 70q^{66} + 152q^{67} - 220q^{68} + 242q^{69} - 254q^{70} + 72q^{71} - 150q^{72} + 156q^{73} - 288q^{74} + 8q^{75} - 500q^{76} + 444q^{77} - 194q^{78} + 192q^{79} - 152q^{80} - 88q^{81} - 688q^{82} + 180q^{83} - 346q^{84} + 284q^{85} - 380q^{86} + 176q^{87} - 532q^{88} + 284q^{89} - 210q^{90} + 192q^{91} - 292q^{92} + 144q^{93} - 352q^{94} + 162q^{95} - 380q^{96} + 100q^{97} - 48q^{98} + 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1140))$$

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
1140.2.a $$\chi_{1140}(1, \cdot)$$ 1140.2.a.a 1 1
1140.2.a.b 1
1140.2.a.c 1
1140.2.a.d 1
1140.2.a.e 2
1140.2.a.f 3
1140.2.a.g 3
1140.2.b $$\chi_{1140}(151, \cdot)$$ 1140.2.b.a 2 1
1140.2.b.b 2
1140.2.b.c 18
1140.2.b.d 18
1140.2.b.e 20
1140.2.b.f 20
1140.2.e $$\chi_{1140}(569, \cdot)$$ 1140.2.e.a 16 1
1140.2.e.b 24
1140.2.f $$\chi_{1140}(229, \cdot)$$ 1140.2.f.a 6 1
1140.2.f.b 10
1140.2.i $$\chi_{1140}(191, \cdot)$$ n/a 144 1
1140.2.j $$\chi_{1140}(341, \cdot)$$ 1140.2.j.a 28 1
1140.2.m $$\chi_{1140}(379, \cdot)$$ n/a 120 1
1140.2.n $$\chi_{1140}(419, \cdot)$$ n/a 216 1
1140.2.q $$\chi_{1140}(121, \cdot)$$ 1140.2.q.a 2 2
1140.2.q.b 2
1140.2.q.c 2
1140.2.q.d 2
1140.2.q.e 2
1140.2.q.f 2
1140.2.q.g 2
1140.2.q.h 2
1140.2.q.i 2
1140.2.q.j 2
1140.2.q.k 2
1140.2.q.l 2
1140.2.s $$\chi_{1140}(343, \cdot)$$ n/a 216 2
1140.2.u $$\chi_{1140}(77, \cdot)$$ 1140.2.u.a 36 2
1140.2.u.b 36
1140.2.w $$\chi_{1140}(227, \cdot)$$ n/a 464 2
1140.2.y $$\chi_{1140}(37, \cdot)$$ 1140.2.y.a 40 2
1140.2.z $$\chi_{1140}(449, \cdot)$$ 1140.2.z.a 80 2
1140.2.bc $$\chi_{1140}(31, \cdot)$$ n/a 160 2
1140.2.bd $$\chi_{1140}(11, \cdot)$$ n/a 320 2
1140.2.bg $$\chi_{1140}(49, \cdot)$$ 1140.2.bg.a 4 2
1140.2.bg.b 4
1140.2.bg.c 32
1140.2.bh $$\chi_{1140}(259, \cdot)$$ n/a 240 2
1140.2.bk $$\chi_{1140}(221, \cdot)$$ 1140.2.bk.a 56 2
1140.2.bn $$\chi_{1140}(239, \cdot)$$ n/a 464 2
1140.2.bo $$\chi_{1140}(61, \cdot)$$ 1140.2.bo.a 18 6
1140.2.bo.b 18
1140.2.bo.c 24
1140.2.bo.d 24
1140.2.bp $$\chi_{1140}(197, \cdot)$$ n/a 160 4
1140.2.br $$\chi_{1140}(7, \cdot)$$ n/a 480 4
1140.2.bt $$\chi_{1140}(217, \cdot)$$ 1140.2.bt.a 80 4
1140.2.bv $$\chi_{1140}(107, \cdot)$$ n/a 928 4
1140.2.bz $$\chi_{1140}(119, \cdot)$$ n/a 1392 6
1140.2.ca $$\chi_{1140}(79, \cdot)$$ n/a 720 6
1140.2.cd $$\chi_{1140}(41, \cdot)$$ n/a 156 6
1140.2.cf $$\chi_{1140}(169, \cdot)$$ n/a 120 6
1140.2.cg $$\chi_{1140}(131, \cdot)$$ n/a 960 6
1140.2.cj $$\chi_{1140}(91, \cdot)$$ n/a 480 6
1140.2.ck $$\chi_{1140}(29, \cdot)$$ n/a 240 6
1140.2.cm $$\chi_{1140}(143, \cdot)$$ n/a 2784 12
1140.2.co $$\chi_{1140}(13, \cdot)$$ n/a 240 12
1140.2.cq $$\chi_{1140}(17, \cdot)$$ n/a 480 12
1140.2.cs $$\chi_{1140}(43, \cdot)$$ n/a 1440 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1140))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1140)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(570))$$$$^{\oplus 2}$$