# Properties

 Label 2184.2 Level 2184 Weight 2 Dimension 51104 Nonzero newspaces 90 Sturm bound 516096 Trace bound 24

## Defining parameters

 Level: $$N$$ = $$2184 = 2^{3} \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$90$$ Sturm bound: $$516096$$ Trace bound: $$24$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2184))$$.

Total New Old
Modular forms 132480 51984 80496
Cusp forms 125569 51104 74465
Eisenstein series 6911 880 6031

## Trace form

 $$51104 q - 8 q^{2} - 48 q^{3} - 88 q^{4} - 8 q^{5} - 28 q^{6} - 104 q^{7} + 16 q^{8} - 96 q^{9} + O(q^{10})$$ $$51104 q - 8 q^{2} - 48 q^{3} - 88 q^{4} - 8 q^{5} - 28 q^{6} - 104 q^{7} + 16 q^{8} - 96 q^{9} - 56 q^{10} - 8 q^{11} - 4 q^{12} - 16 q^{13} + 8 q^{14} - 96 q^{15} - 72 q^{16} - 44 q^{17} - 60 q^{18} - 120 q^{19} + 40 q^{20} - 24 q^{21} - 104 q^{22} + 24 q^{23} - 12 q^{24} - 168 q^{25} + 44 q^{26} - 96 q^{27} + 96 q^{28} - 36 q^{29} + 44 q^{30} + 24 q^{31} + 152 q^{32} - 44 q^{33} + 152 q^{34} + 48 q^{35} - 56 q^{36} + 36 q^{37} + 104 q^{38} + 12 q^{39} + 176 q^{40} + 28 q^{41} - 40 q^{42} - 16 q^{43} + 144 q^{44} + 112 q^{45} + 256 q^{46} + 192 q^{47} + 4 q^{48} - 108 q^{49} + 256 q^{50} + 216 q^{51} + 272 q^{52} + 208 q^{53} - 204 q^{54} + 328 q^{55} + 32 q^{56} - 88 q^{57} + 144 q^{58} + 304 q^{59} + 172 q^{61} + 8 q^{62} + 104 q^{63} - 136 q^{64} + 76 q^{65} - 148 q^{66} + 120 q^{67} - 120 q^{68} + 56 q^{69} - 88 q^{70} + 128 q^{71} - 216 q^{72} - 232 q^{73} + 64 q^{74} + 104 q^{75} - 168 q^{76} - 72 q^{77} - 176 q^{78} - 216 q^{79} - 80 q^{81} - 216 q^{82} - 112 q^{83} - 364 q^{84} - 124 q^{85} - 224 q^{86} - 248 q^{88} - 8 q^{89} - 592 q^{90} - 24 q^{91} - 312 q^{92} + 52 q^{93} - 504 q^{94} + 208 q^{95} - 660 q^{96} + 80 q^{97} - 344 q^{98} + 24 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2184))$$

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
2184.2.a $$\chi_{2184}(1, \cdot)$$ 2184.2.a.a 1 1
2184.2.a.b 1
2184.2.a.c 1
2184.2.a.d 1
2184.2.a.e 1
2184.2.a.f 1
2184.2.a.g 1
2184.2.a.h 1
2184.2.a.i 1
2184.2.a.j 1
2184.2.a.k 1
2184.2.a.l 1
2184.2.a.m 1
2184.2.a.n 2
2184.2.a.o 2
2184.2.a.p 2
2184.2.a.q 2
2184.2.a.r 2
2184.2.a.s 3
2184.2.a.t 3
2184.2.a.u 3
2184.2.a.v 4
2184.2.b $$\chi_{2184}(1819, \cdot)$$ n/a 224 1
2184.2.e $$\chi_{2184}(391, \cdot)$$ None 0 1
2184.2.g $$\chi_{2184}(1093, \cdot)$$ n/a 144 1
2184.2.h $$\chi_{2184}(337, \cdot)$$ 2184.2.h.a 2 1
2184.2.h.b 2
2184.2.h.c 4
2184.2.h.d 6
2184.2.h.e 10
2184.2.h.f 10
2184.2.h.g 10
2184.2.j $$\chi_{2184}(911, \cdot)$$ None 0 1
2184.2.m $$\chi_{2184}(155, \cdot)$$ n/a 336 1
2184.2.o $$\chi_{2184}(545, \cdot)$$ n/a 112 1
2184.2.p $$\chi_{2184}(1301, \cdot)$$ n/a 384 1
2184.2.s $$\chi_{2184}(1247, \cdot)$$ None 0 1
2184.2.t $$\chi_{2184}(2003, \cdot)$$ n/a 288 1
2184.2.v $$\chi_{2184}(209, \cdot)$$ 2184.2.v.a 48 1
2184.2.v.b 48
2184.2.y $$\chi_{2184}(1637, \cdot)$$ n/a 440 1
2184.2.ba $$\chi_{2184}(1483, \cdot)$$ n/a 192 1
2184.2.bb $$\chi_{2184}(727, \cdot)$$ None 0 1
2184.2.bd $$\chi_{2184}(1429, \cdot)$$ n/a 168 1
2184.2.bg $$\chi_{2184}(625, \cdot)$$ 2184.2.bg.a 2 2
2184.2.bg.b 2
2184.2.bg.c 2
2184.2.bg.d 2
2184.2.bg.e 4
2184.2.bg.f 4
2184.2.bg.g 6
2184.2.bg.h 6
2184.2.bg.i 8
2184.2.bg.j 10
2184.2.bg.k 12
2184.2.bg.l 12
2184.2.bg.m 12
2184.2.bg.n 14
2184.2.bh $$\chi_{2184}(289, \cdot)$$ n/a 112 2
2184.2.bi $$\chi_{2184}(1465, \cdot)$$ n/a 112 2
2184.2.bj $$\chi_{2184}(841, \cdot)$$ 2184.2.bj.a 2 2
2184.2.bj.b 2
2184.2.bj.c 2
2184.2.bj.d 2
2184.2.bj.e 2
2184.2.bj.f 4
2184.2.bj.g 6
2184.2.bj.h 8
2184.2.bj.i 8
2184.2.bj.j 8
2184.2.bj.k 8
2184.2.bj.l 8
2184.2.bj.m 10
2184.2.bj.n 10
2184.2.bk $$\chi_{2184}(671, \cdot)$$ None 0 2
2184.2.bm $$\chi_{2184}(83, \cdot)$$ n/a 880 2
2184.2.bo $$\chi_{2184}(1555, \cdot)$$ n/a 336 2
2184.2.bq $$\chi_{2184}(463, \cdot)$$ None 0 2
2184.2.bt $$\chi_{2184}(853, \cdot)$$ n/a 448 2
2184.2.bv $$\chi_{2184}(265, \cdot)$$ n/a 112 2
2184.2.bx $$\chi_{2184}(281, \cdot)$$ n/a 168 2
2184.2.bz $$\chi_{2184}(1373, \cdot)$$ n/a 672 2
2184.2.ca $$\chi_{2184}(965, \cdot)$$ n/a 880 2
2184.2.cd $$\chi_{2184}(881, \cdot)$$ n/a 224 2
2184.2.cf $$\chi_{2184}(491, \cdot)$$ n/a 672 2
2184.2.cg $$\chi_{2184}(575, \cdot)$$ None 0 2
2184.2.ci $$\chi_{2184}(673, \cdot)$$ 2184.2.ci.a 20 2
2184.2.ci.b 20
2184.2.ci.c 24
2184.2.ci.d 24
2184.2.cl $$\chi_{2184}(757, \cdot)$$ n/a 336 2
2184.2.cn $$\chi_{2184}(55, \cdot)$$ None 0 2
2184.2.co $$\chi_{2184}(979, \cdot)$$ n/a 448 2
2184.2.cq $$\chi_{2184}(101, \cdot)$$ n/a 880 2
2184.2.ct $$\chi_{2184}(185, \cdot)$$ n/a 224 2
2184.2.cv $$\chi_{2184}(1283, \cdot)$$ n/a 880 2
2184.2.cw $$\chi_{2184}(1031, \cdot)$$ None 0 2
2184.2.cz $$\chi_{2184}(199, \cdot)$$ None 0 2
2184.2.da $$\chi_{2184}(451, \cdot)$$ n/a 448 2
2184.2.dd $$\chi_{2184}(1117, \cdot)$$ n/a 448 2
2184.2.df $$\chi_{2184}(859, \cdot)$$ n/a 384 2
2184.2.di $$\chi_{2184}(103, \cdot)$$ None 0 2
2184.2.dl $$\chi_{2184}(205, \cdot)$$ n/a 448 2
2184.2.dn $$\chi_{2184}(107, \cdot)$$ n/a 880 2
2184.2.do $$\chi_{2184}(23, \cdot)$$ None 0 2
2184.2.dr $$\chi_{2184}(521, \cdot)$$ n/a 192 2
2184.2.ds $$\chi_{2184}(1013, \cdot)$$ n/a 880 2
2184.2.du $$\chi_{2184}(935, \cdot)$$ None 0 2
2184.2.dx $$\chi_{2184}(443, \cdot)$$ n/a 768 2
2184.2.dy $$\chi_{2184}(1109, \cdot)$$ n/a 880 2
2184.2.eb $$\chi_{2184}(1361, \cdot)$$ n/a 224 2
2184.2.ee $$\chi_{2184}(1213, \cdot)$$ n/a 448 2
2184.2.eg $$\chi_{2184}(1375, \cdot)$$ None 0 2
2184.2.eh $$\chi_{2184}(1459, \cdot)$$ n/a 448 2
2184.2.ek $$\chi_{2184}(121, \cdot)$$ n/a 112 2
2184.2.el $$\chi_{2184}(373, \cdot)$$ n/a 448 2
2184.2.en $$\chi_{2184}(367, \cdot)$$ None 0 2
2184.2.eq $$\chi_{2184}(283, \cdot)$$ n/a 448 2
2184.2.er $$\chi_{2184}(1115, \cdot)$$ n/a 880 2
2184.2.eu $$\chi_{2184}(1199, \cdot)$$ None 0 2
2184.2.ev $$\chi_{2184}(857, \cdot)$$ n/a 224 2
2184.2.ey $$\chi_{2184}(677, \cdot)$$ n/a 768 2
2184.2.fa $$\chi_{2184}(599, \cdot)$$ None 0 2
2184.2.fb $$\chi_{2184}(779, \cdot)$$ n/a 880 2
2184.2.fe $$\chi_{2184}(269, \cdot)$$ n/a 880 2
2184.2.ff $$\chi_{2184}(17, \cdot)$$ n/a 224 2
2184.2.fh $$\chi_{2184}(1543, \cdot)$$ None 0 2
2184.2.fk $$\chi_{2184}(1291, \cdot)$$ n/a 448 2
2184.2.fl $$\chi_{2184}(781, \cdot)$$ n/a 384 2
2184.2.fo $$\chi_{2184}(25, \cdot)$$ n/a 112 2
2184.2.fq $$\chi_{2184}(1195, \cdot)$$ n/a 448 2
2184.2.fr $$\chi_{2184}(703, \cdot)$$ None 0 2
2184.2.fu $$\chi_{2184}(1297, \cdot)$$ n/a 112 2
2184.2.fv $$\chi_{2184}(1381, \cdot)$$ n/a 448 2
2184.2.fy $$\chi_{2184}(1277, \cdot)$$ n/a 880 2
2184.2.fz $$\chi_{2184}(1193, \cdot)$$ n/a 224 2
2184.2.gb $$\chi_{2184}(179, \cdot)$$ n/a 880 2
2184.2.ge $$\chi_{2184}(191, \cdot)$$ None 0 2
2184.2.gg $$\chi_{2184}(589, \cdot)$$ n/a 336 2
2184.2.gi $$\chi_{2184}(1063, \cdot)$$ None 0 2
2184.2.gl $$\chi_{2184}(139, \cdot)$$ n/a 448 2
2184.2.gn $$\chi_{2184}(797, \cdot)$$ n/a 880 2
2184.2.go $$\chi_{2184}(1049, \cdot)$$ n/a 224 2
2184.2.gq $$\chi_{2184}(659, \cdot)$$ n/a 672 2
2184.2.gt $$\chi_{2184}(407, \cdot)$$ None 0 2
2184.2.gv $$\chi_{2184}(59, \cdot)$$ n/a 1760 4
2184.2.gx $$\chi_{2184}(1055, \cdot)$$ None 0 4
2184.2.gz $$\chi_{2184}(319, \cdot)$$ None 0 4
2184.2.hb $$\chi_{2184}(1003, \cdot)$$ n/a 896 4
2184.2.hd $$\chi_{2184}(197, \cdot)$$ n/a 1344 4
2184.2.hf $$\chi_{2184}(449, \cdot)$$ n/a 336 4
2184.2.hg $$\chi_{2184}(473, \cdot)$$ n/a 448 4
2184.2.hi $$\chi_{2184}(149, \cdot)$$ n/a 1760 4
2184.2.hk $$\chi_{2184}(977, \cdot)$$ n/a 448 4
2184.2.hm $$\chi_{2184}(317, \cdot)$$ n/a 1760 4
2184.2.hp $$\chi_{2184}(97, \cdot)$$ n/a 224 4
2184.2.hr $$\chi_{2184}(349, \cdot)$$ n/a 896 4
2184.2.hs $$\chi_{2184}(229, \cdot)$$ n/a 896 4
2184.2.hu $$\chi_{2184}(1081, \cdot)$$ n/a 224 4
2184.2.hw $$\chi_{2184}(397, \cdot)$$ n/a 896 4
2184.2.hy $$\chi_{2184}(73, \cdot)$$ n/a 224 4
2184.2.ia $$\chi_{2184}(631, \cdot)$$ None 0 4
2184.2.ic $$\chi_{2184}(379, \cdot)$$ n/a 672 4
2184.2.if $$\chi_{2184}(499, \cdot)$$ n/a 896 4
2184.2.ih $$\chi_{2184}(1159, \cdot)$$ None 0 4
2184.2.ij $$\chi_{2184}(67, \cdot)$$ n/a 896 4
2184.2.il $$\chi_{2184}(151, \cdot)$$ None 0 4
2184.2.im $$\chi_{2184}(587, \cdot)$$ n/a 1760 4
2184.2.io $$\chi_{2184}(167, \cdot)$$ None 0 4
2184.2.ir $$\chi_{2184}(47, \cdot)$$ None 0 4
2184.2.it $$\chi_{2184}(899, \cdot)$$ n/a 1760 4
2184.2.iv $$\chi_{2184}(215, \cdot)$$ None 0 4
2184.2.ix $$\chi_{2184}(395, \cdot)$$ n/a 1760 4
2184.2.iy $$\chi_{2184}(145, \cdot)$$ n/a 224 4
2184.2.ja $$\chi_{2184}(1237, \cdot)$$ n/a 896 4
2184.2.jc $$\chi_{2184}(821, \cdot)$$ n/a 1760 4
2184.2.je $$\chi_{2184}(137, \cdot)$$ n/a 448 4

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2184))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2184)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(273))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(364))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(546))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(728))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1092))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2184))$$$$^{\oplus 1}$$