# Properties

 Label 2160.2 Level 2160 Weight 2 Dimension 50256 Nonzero newspaces 42 Sturm bound 497664 Trace bound 31

## Defining parameters

 Level: $$N$$ = $$2160 = 2^{4} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$42$$ Sturm bound: $$497664$$ Trace bound: $$31$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2160))$$.

Total New Old
Modular forms 127776 51120 76656
Cusp forms 121057 50256 70801
Eisenstein series 6719 864 5855

## Trace form

 $$50256 q - 32 q^{2} - 36 q^{3} - 56 q^{4} - 59 q^{5} - 144 q^{6} - 38 q^{7} - 32 q^{8} - 12 q^{9} + O(q^{10})$$ $$50256 q - 32 q^{2} - 36 q^{3} - 56 q^{4} - 59 q^{5} - 144 q^{6} - 38 q^{7} - 32 q^{8} - 12 q^{9} - 84 q^{10} - 62 q^{11} - 48 q^{12} - 62 q^{13} - 48 q^{14} - 54 q^{15} - 184 q^{16} - 90 q^{17} - 48 q^{18} - 46 q^{19} - 76 q^{20} - 180 q^{21} - 104 q^{22} - 46 q^{23} - 48 q^{24} - 37 q^{25} - 160 q^{26} - 72 q^{27} - 176 q^{28} - 154 q^{29} - 72 q^{30} - 178 q^{31} - 72 q^{32} - 156 q^{33} - 72 q^{34} - 121 q^{35} - 144 q^{36} - 142 q^{37} + 24 q^{38} - 108 q^{39} - 52 q^{40} - 110 q^{41} - 48 q^{42} - 166 q^{43} + 56 q^{44} - 114 q^{45} - 72 q^{46} - 190 q^{47} - 48 q^{48} - 156 q^{49} - 4 q^{50} - 90 q^{51} + 8 q^{52} - 80 q^{53} - 48 q^{54} - 210 q^{55} + 264 q^{56} + 18 q^{57} + 136 q^{58} - 58 q^{59} + 48 q^{60} - 106 q^{61} + 448 q^{62} + 24 q^{63} + 88 q^{64} + 15 q^{65} + 216 q^{66} + 2 q^{67} + 520 q^{68} + 132 q^{69} + 108 q^{70} + 118 q^{71} + 288 q^{72} + 82 q^{73} + 528 q^{74} - 12 q^{75} + 216 q^{76} + 258 q^{77} + 264 q^{78} + 74 q^{79} + 284 q^{80} - 132 q^{81} + 96 q^{82} + 170 q^{83} + 216 q^{84} - 59 q^{85} + 408 q^{86} + 152 q^{88} + 130 q^{89} + 36 q^{90} - 6 q^{91} + 152 q^{92} + 84 q^{93} + 8 q^{94} + 145 q^{95} - 144 q^{96} - 174 q^{97} + 176 q^{98} + 180 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2160))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2160.2.a $$\chi_{2160}(1, \cdot)$$ 2160.2.a.a 1 1
2160.2.a.b 1
2160.2.a.c 1
2160.2.a.d 1
2160.2.a.e 1
2160.2.a.f 1
2160.2.a.g 1
2160.2.a.h 1
2160.2.a.i 1
2160.2.a.j 1
2160.2.a.k 1
2160.2.a.l 1
2160.2.a.m 1
2160.2.a.n 1
2160.2.a.o 1
2160.2.a.p 1
2160.2.a.q 1
2160.2.a.r 1
2160.2.a.s 1
2160.2.a.t 1
2160.2.a.u 1
2160.2.a.v 1
2160.2.a.w 1
2160.2.a.x 1
2160.2.a.y 2
2160.2.a.z 2
2160.2.a.ba 2
2160.2.a.bb 2
2160.2.b $$\chi_{2160}(1511, \cdot)$$ None 0 1
2160.2.d $$\chi_{2160}(649, \cdot)$$ None 0 1
2160.2.f $$\chi_{2160}(1729, \cdot)$$ 2160.2.f.a 2 1
2160.2.f.b 2
2160.2.f.c 2
2160.2.f.d 2
2160.2.f.e 2
2160.2.f.f 2
2160.2.f.g 2
2160.2.f.h 2
2160.2.f.i 4
2160.2.f.j 4
2160.2.f.k 4
2160.2.f.l 4
2160.2.f.m 4
2160.2.f.n 4
2160.2.f.o 8
2160.2.h $$\chi_{2160}(431, \cdot)$$ 2160.2.h.a 4 1
2160.2.h.b 4
2160.2.h.c 4
2160.2.h.d 4
2160.2.h.e 4
2160.2.h.f 4
2160.2.h.g 8
2160.2.k $$\chi_{2160}(1081, \cdot)$$ None 0 1
2160.2.m $$\chi_{2160}(1079, \cdot)$$ None 0 1
2160.2.o $$\chi_{2160}(2159, \cdot)$$ 2160.2.o.a 4 1
2160.2.o.b 4
2160.2.o.c 4
2160.2.o.d 4
2160.2.o.e 8
2160.2.o.f 8
2160.2.o.g 8
2160.2.o.h 8
2160.2.q $$\chi_{2160}(721, \cdot)$$ 2160.2.q.a 2 2
2160.2.q.b 2
2160.2.q.c 2
2160.2.q.d 2
2160.2.q.e 2
2160.2.q.f 4
2160.2.q.g 4
2160.2.q.h 4
2160.2.q.i 6
2160.2.q.j 6
2160.2.q.k 6
2160.2.q.l 8
2160.2.t $$\chi_{2160}(541, \cdot)$$ n/a 256 2
2160.2.u $$\chi_{2160}(539, \cdot)$$ n/a 384 2
2160.2.w $$\chi_{2160}(593, \cdot)$$ 2160.2.w.a 8 2
2160.2.w.b 8
2160.2.w.c 8
2160.2.w.d 8
2160.2.w.e 8
2160.2.w.f 8
2160.2.w.g 24
2160.2.w.h 24
2160.2.x $$\chi_{2160}(703, \cdot)$$ 2160.2.x.a 8 2
2160.2.x.b 8
2160.2.x.c 8
2160.2.x.d 8
2160.2.x.e 16
2160.2.x.f 16
2160.2.x.g 32
2160.2.z $$\chi_{2160}(163, \cdot)$$ n/a 384 2
2160.2.bc $$\chi_{2160}(917, \cdot)$$ n/a 384 2
2160.2.bd $$\chi_{2160}(1027, \cdot)$$ n/a 384 2
2160.2.bg $$\chi_{2160}(53, \cdot)$$ n/a 384 2
2160.2.bi $$\chi_{2160}(487, \cdot)$$ None 0 2
2160.2.bj $$\chi_{2160}(377, \cdot)$$ None 0 2
2160.2.bl $$\chi_{2160}(971, \cdot)$$ n/a 256 2
2160.2.bm $$\chi_{2160}(109, \cdot)$$ n/a 384 2
2160.2.br $$\chi_{2160}(719, \cdot)$$ 2160.2.br.a 8 2
2160.2.br.b 16
2160.2.br.c 24
2160.2.br.d 24
2160.2.bt $$\chi_{2160}(359, \cdot)$$ None 0 2
2160.2.bv $$\chi_{2160}(361, \cdot)$$ None 0 2
2160.2.bw $$\chi_{2160}(1151, \cdot)$$ 2160.2.bw.a 16 2
2160.2.bw.b 16
2160.2.bw.c 16
2160.2.by $$\chi_{2160}(289, \cdot)$$ 2160.2.by.a 4 2
2160.2.by.b 4
2160.2.by.c 8
2160.2.by.d 8
2160.2.by.e 12
2160.2.by.f 32
2160.2.ca $$\chi_{2160}(1369, \cdot)$$ None 0 2
2160.2.cc $$\chi_{2160}(71, \cdot)$$ None 0 2
2160.2.ce $$\chi_{2160}(241, \cdot)$$ n/a 432 6
2160.2.cf $$\chi_{2160}(469, \cdot)$$ n/a 560 4
2160.2.cg $$\chi_{2160}(251, \cdot)$$ n/a 384 4
2160.2.cj $$\chi_{2160}(343, \cdot)$$ None 0 4
2160.2.cm $$\chi_{2160}(233, \cdot)$$ None 0 4
2160.2.cn $$\chi_{2160}(557, \cdot)$$ n/a 560 4
2160.2.cq $$\chi_{2160}(307, \cdot)$$ n/a 560 4
2160.2.cr $$\chi_{2160}(197, \cdot)$$ n/a 560 4
2160.2.cu $$\chi_{2160}(667, \cdot)$$ n/a 560 4
2160.2.cv $$\chi_{2160}(17, \cdot)$$ n/a 136 4
2160.2.cy $$\chi_{2160}(127, \cdot)$$ n/a 144 4
2160.2.db $$\chi_{2160}(179, \cdot)$$ n/a 560 4
2160.2.dc $$\chi_{2160}(181, \cdot)$$ n/a 384 4
2160.2.dd $$\chi_{2160}(119, \cdot)$$ None 0 6
2160.2.di $$\chi_{2160}(121, \cdot)$$ None 0 6
2160.2.dj $$\chi_{2160}(239, \cdot)$$ n/a 648 6
2160.2.dm $$\chi_{2160}(49, \cdot)$$ n/a 636 6
2160.2.dn $$\chi_{2160}(311, \cdot)$$ None 0 6
2160.2.do $$\chi_{2160}(191, \cdot)$$ n/a 432 6
2160.2.dp $$\chi_{2160}(169, \cdot)$$ None 0 6
2160.2.du $$\chi_{2160}(59, \cdot)$$ n/a 5136 12
2160.2.dv $$\chi_{2160}(61, \cdot)$$ n/a 3456 12
2160.2.dy $$\chi_{2160}(137, \cdot)$$ None 0 12
2160.2.dz $$\chi_{2160}(223, \cdot)$$ n/a 1296 12
2160.2.ea $$\chi_{2160}(43, \cdot)$$ n/a 5136 12
2160.2.ec $$\chi_{2160}(77, \cdot)$$ n/a 5136 12
2160.2.ee $$\chi_{2160}(173, \cdot)$$ n/a 5136 12
2160.2.eg $$\chi_{2160}(187, \cdot)$$ n/a 5136 12
2160.2.ek $$\chi_{2160}(113, \cdot)$$ n/a 1272 12
2160.2.el $$\chi_{2160}(7, \cdot)$$ None 0 12
2160.2.eo $$\chi_{2160}(229, \cdot)$$ n/a 5136 12
2160.2.ep $$\chi_{2160}(11, \cdot)$$ n/a 3456 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2160))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2160)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 40}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(270))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(432))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(540))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(720))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1080))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2160))$$$$^{\oplus 1}$$