↑

Properties

Label 1184.2
Level 1184
Weight 2
Dimension 24238
Nonzero newspaces 30
Sturm bound 175104
Trace bound 20

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1184 = 2^{5} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(175104\)
Trace bound: \(20\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1184))\).

Total New Old
Modular forms 44928 24938 19990
Cusp forms 42625 24238 18387
Eisenstein series 2303 700 1603

Trace form

\( 24238 q - 136 q^{2} - 100 q^{3} - 136 q^{4} - 132 q^{5} - 136 q^{6} - 100 q^{7} - 136 q^{8} - 202 q^{9} + O(q^{10}) \) \( 24238 q - 136 q^{2} - 100 q^{3} - 136 q^{4} - 132 q^{5} - 136 q^{6} - 100 q^{7} - 136 q^{8} - 202 q^{9} - 152 q^{10} - 100 q^{11} - 168 q^{12} - 148 q^{13} - 168 q^{14} - 108 q^{15} - 176 q^{16} - 76 q^{17} - 176 q^{18} - 100 q^{19} - 168 q^{20} - 136 q^{21} - 160 q^{22} - 116 q^{23} - 112 q^{24} - 206 q^{25} - 96 q^{26} - 148 q^{27} - 96 q^{28} - 116 q^{29} - 72 q^{30} - 140 q^{31} - 96 q^{32} - 344 q^{33} - 112 q^{34} - 148 q^{35} - 80 q^{36} - 138 q^{37} - 296 q^{38} - 148 q^{39} - 160 q^{40} - 228 q^{41} - 176 q^{42} - 116 q^{43} - 216 q^{44} - 172 q^{45} - 200 q^{46} - 108 q^{47} - 240 q^{48} - 58 q^{49} - 216 q^{50} - 92 q^{51} - 152 q^{52} - 196 q^{53} - 160 q^{54} - 36 q^{55} - 160 q^{56} - 208 q^{57} - 128 q^{58} - 36 q^{59} - 128 q^{60} - 180 q^{61} - 96 q^{62} - 12 q^{63} - 64 q^{64} - 320 q^{65} - 88 q^{66} - 20 q^{67} - 176 q^{68} - 200 q^{69} - 112 q^{70} - 36 q^{71} - 184 q^{72} - 196 q^{73} - 156 q^{74} - 184 q^{75} - 136 q^{76} - 168 q^{77} - 216 q^{78} - 108 q^{79} - 128 q^{80} - 90 q^{81} - 136 q^{82} - 180 q^{83} - 176 q^{84} - 168 q^{85} - 96 q^{86} - 212 q^{87} - 144 q^{88} - 228 q^{89} - 160 q^{90} - 196 q^{91} - 64 q^{92} - 112 q^{93} - 160 q^{94} - 220 q^{95} - 144 q^{96} - 380 q^{97} - 96 q^{98} - 204 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1184))\)

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
1184.2.a \(\chi_{1184}(1, \cdot)\) 1184.2.a.a 1 1
1184.2.a.b 1
1184.2.a.c 1
1184.2.a.d 1
1184.2.a.e 1
1184.2.a.f 1
1184.2.a.g 1
1184.2.a.h 1
1184.2.a.i 2
1184.2.a.j 2
1184.2.a.k 2
1184.2.a.l 3
1184.2.a.m 3
1184.2.a.n 4
1184.2.a.o 4
1184.2.a.p 8
1184.2.c \(\chi_{1184}(593, \cdot)\) 1184.2.c.a 4 1
1184.2.c.b 4
1184.2.c.c 28
1184.2.e \(\chi_{1184}(369, \cdot)\) 1184.2.e.a 36 1
1184.2.g \(\chi_{1184}(961, \cdot)\) 1184.2.g.a 2 1
1184.2.g.b 2
1184.2.g.c 2
1184.2.g.d 4
1184.2.g.e 6
1184.2.g.f 6
1184.2.g.g 8
1184.2.g.h 8
1184.2.i \(\chi_{1184}(417, \cdot)\) 1184.2.i.a 2 2
1184.2.i.b 2
1184.2.i.c 4
1184.2.i.d 4
1184.2.i.e 6
1184.2.i.f 6
1184.2.i.g 8
1184.2.i.h 8
1184.2.i.i 18
1184.2.i.j 18
1184.2.j \(\chi_{1184}(623, \cdot)\) 1184.2.j.a 8 2
1184.2.j.b 64
1184.2.m \(\chi_{1184}(487, \cdot)\) None 0 2
1184.2.n \(\chi_{1184}(73, \cdot)\) None 0 2
1184.2.o \(\chi_{1184}(297, \cdot)\) None 0 2
1184.2.s \(\chi_{1184}(327, \cdot)\) None 0 2
1184.2.t \(\chi_{1184}(31, \cdot)\) 1184.2.t.a 4 2
1184.2.t.b 4
1184.2.t.c 6
1184.2.t.d 6
1184.2.t.e 14
1184.2.t.f 14
1184.2.t.g 14
1184.2.t.h 14
1184.2.w \(\chi_{1184}(545, \cdot)\) 1184.2.w.a 4 2
1184.2.w.b 4
1184.2.w.c 32
1184.2.w.d 36
1184.2.y \(\chi_{1184}(529, \cdot)\) 1184.2.y.a 72 2
1184.2.ba \(\chi_{1184}(433, \cdot)\) 1184.2.ba.a 72 2
1184.2.bc \(\chi_{1184}(149, \cdot)\) n/a 576 4
1184.2.bf \(\chi_{1184}(43, \cdot)\) n/a 600 4
1184.2.bh \(\chi_{1184}(339, \cdot)\) n/a 600 4
1184.2.bj \(\chi_{1184}(221, \cdot)\) n/a 600 4
1184.2.bk \(\chi_{1184}(33, \cdot)\) n/a 228 6
1184.2.bm \(\chi_{1184}(319, \cdot)\) n/a 152 4
1184.2.bn \(\chi_{1184}(23, \cdot)\) None 0 4
1184.2.br \(\chi_{1184}(121, \cdot)\) None 0 4
1184.2.bs \(\chi_{1184}(233, \cdot)\) None 0 4
1184.2.bt \(\chi_{1184}(615, \cdot)\) None 0 4
1184.2.bw \(\chi_{1184}(399, \cdot)\) n/a 144 4
1184.2.by \(\chi_{1184}(65, \cdot)\) n/a 228 6
1184.2.ca \(\chi_{1184}(49, \cdot)\) n/a 216 6
1184.2.cd \(\chi_{1184}(337, \cdot)\) n/a 216 6
1184.2.ce \(\chi_{1184}(85, \cdot)\) n/a 1200 8
1184.2.ch \(\chi_{1184}(51, \cdot)\) n/a 1200 8
1184.2.cj \(\chi_{1184}(251, \cdot)\) n/a 1200 8
1184.2.cl \(\chi_{1184}(269, \cdot)\) n/a 1200 8
1184.2.cn \(\chi_{1184}(351, \cdot)\) n/a 456 12
1184.2.co \(\chi_{1184}(25, \cdot)\) None 0 12
1184.2.cq \(\chi_{1184}(39, \cdot)\) None 0 12
1184.2.ct \(\chi_{1184}(55, \cdot)\) None 0 12
1184.2.cu \(\chi_{1184}(9, \cdot)\) None 0 12
1184.2.cx \(\chi_{1184}(15, \cdot)\) n/a 432 12
1184.2.cy \(\chi_{1184}(19, \cdot)\) n/a 3600 24
1184.2.db \(\chi_{1184}(21, \cdot)\) n/a 3600 24
1184.2.dd \(\chi_{1184}(53, \cdot)\) n/a 3600 24
1184.2.de \(\chi_{1184}(59, \cdot)\) n/a 3600 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1184))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1184)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(592))\)\(^{\oplus 2}\)