# Properties

 Label 2873.2 Level 2873 Weight 2 Dimension 331280 Nonzero newspaces 40 Sturm bound 1362816 Trace bound 8

## Defining parameters

 Level: $$N$$ = $$2873 = 13^{2} \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$1362816$$ Trace bound: $$8$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2873))$$.

Total New Old
Modular forms 344352 337414 6938
Cusp forms 337057 331280 5777
Eisenstein series 7295 6134 1161

## Trace form

 $$331280 q - 926 q^{2} - 924 q^{3} - 918 q^{4} - 920 q^{5} - 908 q^{6} - 924 q^{7} - 938 q^{8} - 938 q^{9} + O(q^{10})$$ $$331280 q - 926 q^{2} - 924 q^{3} - 918 q^{4} - 920 q^{5} - 908 q^{6} - 924 q^{7} - 938 q^{8} - 938 q^{9} - 960 q^{10} - 940 q^{11} - 1004 q^{12} - 1032 q^{13} - 1788 q^{14} - 956 q^{15} - 986 q^{16} - 1006 q^{17} - 2082 q^{18} - 980 q^{19} - 1008 q^{20} - 996 q^{21} - 996 q^{22} - 940 q^{23} - 1092 q^{24} - 982 q^{25} - 1068 q^{26} - 1860 q^{27} - 1068 q^{28} - 1000 q^{29} - 1140 q^{30} - 1004 q^{31} - 1126 q^{32} - 1044 q^{33} - 1104 q^{34} - 2100 q^{35} - 1166 q^{36} - 956 q^{37} - 1028 q^{38} - 1072 q^{39} - 1976 q^{40} - 1072 q^{41} - 1196 q^{42} - 1068 q^{43} - 1172 q^{44} - 1128 q^{45} - 1172 q^{46} - 1044 q^{47} - 1220 q^{48} - 1082 q^{49} - 1182 q^{50} - 1114 q^{51} - 2326 q^{52} - 1900 q^{53} - 1220 q^{54} - 1116 q^{55} - 1268 q^{56} - 1164 q^{57} - 1140 q^{58} - 1044 q^{59} - 1412 q^{60} - 1100 q^{61} - 1180 q^{62} - 1236 q^{63} - 1282 q^{64} - 1170 q^{65} - 2140 q^{66} - 1060 q^{67} - 1218 q^{68} - 2228 q^{69} - 1332 q^{70} - 1076 q^{71} - 1482 q^{72} - 1156 q^{73} - 1280 q^{74} - 1300 q^{75} - 1332 q^{76} - 1180 q^{77} - 1356 q^{78} - 1916 q^{79} - 1516 q^{80} - 1210 q^{81} - 1232 q^{82} - 1140 q^{83} - 1540 q^{84} - 1168 q^{85} - 2348 q^{86} - 1268 q^{87} - 1428 q^{88} - 1208 q^{89} - 1580 q^{90} - 1204 q^{91} - 2204 q^{92} - 1308 q^{93} - 1380 q^{94} - 1236 q^{95} - 1676 q^{96} - 1120 q^{97} - 1338 q^{98} - 1372 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2873))$$

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
2873.2.a $$\chi_{2873}(1, \cdot)$$ 2873.2.a.a 1 1
2873.2.a.b 1
2873.2.a.c 1
2873.2.a.d 2
2873.2.a.e 2
2873.2.a.f 2
2873.2.a.g 2
2873.2.a.h 2
2873.2.a.i 2
2873.2.a.j 2
2873.2.a.k 3
2873.2.a.l 4
2873.2.a.m 6
2873.2.a.n 6
2873.2.a.o 6
2873.2.a.p 7
2873.2.a.q 7
2873.2.a.r 10
2873.2.a.s 11
2873.2.a.t 11
2873.2.a.u 12
2873.2.a.v 18
2873.2.a.w 18
2873.2.a.x 22
2873.2.a.y 24
2873.2.a.z 24
2873.2.b $$\chi_{2873}(2872, \cdot)$$ n/a 220 1
2873.2.c $$\chi_{2873}(2534, \cdot)$$ n/a 204 1
2873.2.d $$\chi_{2873}(339, \cdot)$$ n/a 222 1
2873.2.e $$\chi_{2873}(698, \cdot)$$ n/a 412 2
2873.2.f $$\chi_{2873}(846, \cdot)$$ n/a 444 2
2873.2.k $$\chi_{2873}(506, \cdot)$$ n/a 440 2
2873.2.l $$\chi_{2873}(1036, \cdot)$$ n/a 444 2
2873.2.m $$\chi_{2873}(868, \cdot)$$ n/a 412 2
2873.2.n $$\chi_{2873}(1206, \cdot)$$ n/a 440 2
2873.2.p $$\chi_{2873}(168, \cdot)$$ n/a 888 4
2873.2.q $$\chi_{2873}(508, \cdot)$$ n/a 884 4
2873.2.s $$\chi_{2873}(361, \cdot)$$ n/a 880 4
2873.2.x $$\chi_{2873}(191, \cdot)$$ n/a 888 4
2873.2.y $$\chi_{2873}(222, \cdot)$$ n/a 2928 12
2873.2.ba $$\chi_{2873}(99, \cdot)$$ n/a 1768 8
2873.2.bb $$\chi_{2873}(606, \cdot)$$ n/a 1768 8
2873.2.be $$\chi_{2873}(485, \cdot)$$ n/a 1776 8
2873.2.bf $$\chi_{2873}(315, \cdot)$$ n/a 1760 8
2873.2.bh $$\chi_{2873}(118, \cdot)$$ n/a 3240 12
2873.2.bi $$\chi_{2873}(103, \cdot)$$ n/a 2928 12
2873.2.bj $$\chi_{2873}(220, \cdot)$$ n/a 3264 12
2873.2.bk $$\chi_{2873}(35, \cdot)$$ n/a 5808 24
2873.2.bm $$\chi_{2873}(150, \cdot)$$ n/a 3536 16
2873.2.bn $$\chi_{2873}(80, \cdot)$$ n/a 3536 16
2873.2.bp $$\chi_{2873}(38, \cdot)$$ n/a 6528 24
2873.2.bu $$\chi_{2873}(157, \cdot)$$ n/a 6480 24
2873.2.bv $$\chi_{2873}(101, \cdot)$$ n/a 6528 24
2873.2.bw $$\chi_{2873}(69, \cdot)$$ n/a 5808 24
2873.2.bx $$\chi_{2873}(16, \cdot)$$ n/a 6480 24
2873.2.bz $$\chi_{2873}(53, \cdot)$$ n/a 13056 48
2873.2.ca $$\chi_{2873}(25, \cdot)$$ n/a 12960 48
2873.2.cc $$\chi_{2873}(55, \cdot)$$ n/a 12960 48
2873.2.ch $$\chi_{2873}(4, \cdot)$$ n/a 13056 48
2873.2.cj $$\chi_{2873}(5, \cdot)$$ n/a 26016 96
2873.2.ck $$\chi_{2873}(44, \cdot)$$ n/a 26016 96
2873.2.cn $$\chi_{2873}(9, \cdot)$$ n/a 26112 96
2873.2.co $$\chi_{2873}(36, \cdot)$$ n/a 25920 96
2873.2.cr $$\chi_{2873}(7, \cdot)$$ n/a 52032 192
2873.2.cs $$\chi_{2873}(6, \cdot)$$ n/a 52032 192

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2873))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2873)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(221))$$$$^{\oplus 2}$$