# Properties

 Label 1870.2 Level 1870 Weight 2 Dimension 30929 Nonzero newspaces 36 Sturm bound 414720 Trace bound 28

## Defining parameters

 Level: $$N$$ = $$1870 = 2 \cdot 5 \cdot 11 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$414720$$ Trace bound: $$28$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1870))$$.

Total New Old
Modular forms 106240 30929 75311
Cusp forms 101121 30929 70192
Eisenstein series 5119 0 5119

## Trace form

 $$30929q - 3q^{2} - 12q^{3} - 3q^{4} - 3q^{5} + 8q^{6} + 16q^{7} - 3q^{8} + 41q^{9} + O(q^{10})$$ $$30929q - 3q^{2} - 12q^{3} - 3q^{4} - 3q^{5} + 8q^{6} + 16q^{7} - 3q^{8} + 41q^{9} + 25q^{10} + 49q^{11} + 60q^{12} + 62q^{13} + 80q^{14} + 144q^{15} + 13q^{16} + 69q^{17} + 109q^{18} + 64q^{19} + 5q^{20} + 176q^{21} + 9q^{22} + 72q^{23} + 40q^{24} + 149q^{25} + 54q^{26} + 156q^{27} + 16q^{28} + 150q^{29} + 48q^{30} + 152q^{31} + 17q^{32} + 192q^{33} + 5q^{34} + 160q^{35} - 19q^{36} + 94q^{37} + 92q^{38} + 288q^{39} + 17q^{40} + 306q^{41} + 136q^{42} + 132q^{43} + 21q^{44} - 11q^{45} - 24q^{46} + 96q^{47} - 12q^{48} - 75q^{49} - 91q^{50} + 86q^{51} + 6q^{52} + 70q^{53} - 56q^{54} - 123q^{55} - 24q^{56} + 132q^{57} - 122q^{58} + 160q^{59} - 68q^{60} - 34q^{61} + 56q^{62} + 152q^{63} - 3q^{64} - 10q^{65} + 4q^{66} - 20q^{67} - 51q^{68} - 8q^{69} - 216q^{70} + 40q^{71} - 39q^{72} - 286q^{73} - 178q^{74} - 120q^{75} - 20q^{76} + 40q^{77} - 264q^{78} - 232q^{79} - 79q^{80} - 175q^{81} - 258q^{82} - 88q^{83} - 64q^{84} - 429q^{85} - 152q^{87} - 47q^{88} + 50q^{89} - 267q^{90} - 144q^{91} - 16q^{92} - 104q^{93} - 160q^{94} - 224q^{95} - 12q^{96} - 282q^{97} - 135q^{98} - 131q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1870))$$

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
1870.2.a $$\chi_{1870}(1, \cdot)$$ 1870.2.a.a 1 1
1870.2.a.b 1
1870.2.a.c 1
1870.2.a.d 1
1870.2.a.e 1
1870.2.a.f 1
1870.2.a.g 1
1870.2.a.h 1
1870.2.a.i 1
1870.2.a.j 2
1870.2.a.k 2
1870.2.a.l 2
1870.2.a.m 2
1870.2.a.n 3
1870.2.a.o 3
1870.2.a.p 3
1870.2.a.q 3
1870.2.a.r 3
1870.2.a.s 4
1870.2.a.t 4
1870.2.a.u 4
1870.2.a.v 5
1870.2.b $$\chi_{1870}(749, \cdot)$$ 1870.2.b.a 2 1
1870.2.b.b 2
1870.2.b.c 10
1870.2.b.d 14
1870.2.b.e 26
1870.2.b.f 26
1870.2.c $$\chi_{1870}(441, \cdot)$$ 1870.2.c.a 2 1
1870.2.c.b 12
1870.2.c.c 12
1870.2.c.d 16
1870.2.c.e 18
1870.2.h $$\chi_{1870}(1189, \cdot)$$ 1870.2.h.a 46 1
1870.2.h.b 46
1870.2.j $$\chi_{1870}(1033, \cdot)$$ n/a 216 2
1870.2.k $$\chi_{1870}(89, \cdot)$$ n/a 184 2
1870.2.o $$\chi_{1870}(373, \cdot)$$ n/a 216 2
1870.2.p $$\chi_{1870}(307, \cdot)$$ n/a 192 2
1870.2.q $$\chi_{1870}(1101, \cdot)$$ n/a 120 2
1870.2.s $$\chi_{1870}(1143, \cdot)$$ n/a 216 2
1870.2.u $$\chi_{1870}(511, \cdot)$$ n/a 256 4
1870.2.v $$\chi_{1870}(111, \cdot)$$ n/a 240 4
1870.2.z $$\chi_{1870}(417, \cdot)$$ n/a 432 4
1870.2.ba $$\chi_{1870}(43, \cdot)$$ n/a 432 4
1870.2.bb $$\chi_{1870}(529, \cdot)$$ n/a 352 4
1870.2.bd $$\chi_{1870}(169, \cdot)$$ n/a 432 4
1870.2.bi $$\chi_{1870}(951, \cdot)$$ n/a 288 4
1870.2.bj $$\chi_{1870}(69, \cdot)$$ n/a 384 4
1870.2.bl $$\chi_{1870}(133, \cdot)$$ n/a 720 8
1870.2.bn $$\chi_{1870}(131, \cdot)$$ n/a 576 8
1870.2.bp $$\chi_{1870}(109, \cdot)$$ n/a 864 8
1870.2.bq $$\chi_{1870}(23, \cdot)$$ n/a 720 8
1870.2.bt $$\chi_{1870}(123, \cdot)$$ n/a 864 8
1870.2.bv $$\chi_{1870}(81, \cdot)$$ n/a 576 8
1870.2.bw $$\chi_{1870}(613, \cdot)$$ n/a 768 8
1870.2.bx $$\chi_{1870}(237, \cdot)$$ n/a 864 8
1870.2.cb $$\chi_{1870}(489, \cdot)$$ n/a 864 8
1870.2.cc $$\chi_{1870}(13, \cdot)$$ n/a 864 8
1870.2.ce $$\chi_{1870}(9, \cdot)$$ n/a 1728 16
1870.2.ci $$\chi_{1870}(83, \cdot)$$ n/a 1728 16
1870.2.cj $$\chi_{1870}(117, \cdot)$$ n/a 1728 16
1870.2.ck $$\chi_{1870}(291, \cdot)$$ n/a 1152 16
1870.2.cn $$\chi_{1870}(37, \cdot)$$ n/a 3456 32
1870.2.co $$\chi_{1870}(41, \cdot)$$ n/a 2304 32
1870.2.cq $$\chi_{1870}(29, \cdot)$$ n/a 3456 32
1870.2.cs $$\chi_{1870}(3, \cdot)$$ n/a 3456 32

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1870))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1870)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(85))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(170))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(187))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(374))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(935))$$$$^{\oplus 2}$$