Properties

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

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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 the 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

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