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Properties

Label 2240.2
Level 2240
Weight 2
Dimension 72204
Nonzero newspaces 56
Sturm bound 589824
Trace bound 81

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Defining parameters

Level: \( N \) = \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(589824\)
Trace bound: \(81\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2240))\).

Total New Old
Modular forms 150912 73524 77388
Cusp forms 144001 72204 71797
Eisenstein series 6911 1320 5591

Trace form

\( 72204 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 64 q^{7} - 160 q^{8} - 92 q^{9} + O(q^{10}) \) \( 72204 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 64 q^{7} - 160 q^{8} - 92 q^{9} - 96 q^{10} - 160 q^{11} - 64 q^{12} - 96 q^{13} - 80 q^{14} - 192 q^{15} - 192 q^{16} - 144 q^{17} - 64 q^{18} - 80 q^{19} - 96 q^{20} - 232 q^{21} - 128 q^{22} - 56 q^{23} + 96 q^{24} - 88 q^{25} - 32 q^{26} - 24 q^{27} - 96 q^{29} + 64 q^{30} - 56 q^{31} + 96 q^{32} + 56 q^{33} + 96 q^{34} - 88 q^{35} - 160 q^{36} - 32 q^{37} + 96 q^{38} - 40 q^{39} - 16 q^{40} - 240 q^{41} - 168 q^{43} - 32 q^{44} - 104 q^{45} - 192 q^{46} - 120 q^{47} - 64 q^{48} - 172 q^{49} - 288 q^{50} - 40 q^{51} - 256 q^{52} - 160 q^{53} - 320 q^{54} + 64 q^{55} - 352 q^{56} - 176 q^{57} - 352 q^{58} + 224 q^{59} - 288 q^{60} - 224 q^{61} - 192 q^{62} + 128 q^{63} - 544 q^{64} - 204 q^{65} - 512 q^{66} + 400 q^{67} - 256 q^{68} + 80 q^{69} - 216 q^{70} + 16 q^{71} - 352 q^{72} + 48 q^{73} - 288 q^{74} + 244 q^{75} - 448 q^{76} + 24 q^{77} - 256 q^{78} + 216 q^{79} - 16 q^{80} + 4 q^{81} + 256 q^{82} + 112 q^{83} + 144 q^{84} - 32 q^{85} + 224 q^{86} + 168 q^{87} + 256 q^{88} + 240 q^{89} + 192 q^{90} + 40 q^{91} + 448 q^{92} + 384 q^{93} + 320 q^{94} + 132 q^{95} + 352 q^{96} + 368 q^{97} + 192 q^{98} + 360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2240))\)

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
2240.2.a \(\chi_{2240}(1, \cdot)\) 2240.2.a.a 1 1
2240.2.a.b 1
2240.2.a.c 1
2240.2.a.d 1
2240.2.a.e 1
2240.2.a.f 1
2240.2.a.g 1
2240.2.a.h 1
2240.2.a.i 1
2240.2.a.j 1
2240.2.a.k 1
2240.2.a.l 1
2240.2.a.m 1
2240.2.a.n 1
2240.2.a.o 1
2240.2.a.p 1
2240.2.a.q 1
2240.2.a.r 1
2240.2.a.s 1
2240.2.a.t 1
2240.2.a.u 1
2240.2.a.v 1
2240.2.a.w 1
2240.2.a.x 1
2240.2.a.y 1
2240.2.a.z 1
2240.2.a.ba 1
2240.2.a.bb 1
2240.2.a.bc 2
2240.2.a.bd 2
2240.2.a.be 2
2240.2.a.bf 2
2240.2.a.bg 2
2240.2.a.bh 2
2240.2.a.bi 2
2240.2.a.bj 2
2240.2.a.bk 2
2240.2.a.bl 2
2240.2.b \(\chi_{2240}(1121, \cdot)\) 2240.2.b.a 2 1
2240.2.b.b 2
2240.2.b.c 4
2240.2.b.d 4
2240.2.b.e 6
2240.2.b.f 6
2240.2.b.g 12
2240.2.b.h 12
2240.2.e \(\chi_{2240}(2239, \cdot)\) 2240.2.e.a 4 1
2240.2.e.b 4
2240.2.e.c 4
2240.2.e.d 8
2240.2.e.e 8
2240.2.e.f 16
2240.2.e.g 48
2240.2.g \(\chi_{2240}(449, \cdot)\) 2240.2.g.a 2 1
2240.2.g.b 2
2240.2.g.c 2
2240.2.g.d 2
2240.2.g.e 2
2240.2.g.f 2
2240.2.g.g 2
2240.2.g.h 2
2240.2.g.i 4
2240.2.g.j 4
2240.2.g.k 4
2240.2.g.l 6
2240.2.g.m 6
2240.2.g.n 10
2240.2.g.o 10
2240.2.g.p 12
2240.2.h \(\chi_{2240}(671, \cdot)\) 2240.2.h.a 4 1
2240.2.h.b 4
2240.2.h.c 4
2240.2.h.d 4
2240.2.h.e 24
2240.2.h.f 24
2240.2.k \(\chi_{2240}(1791, \cdot)\) 2240.2.k.a 4 1
2240.2.k.b 4
2240.2.k.c 8
2240.2.k.d 8
2240.2.k.e 8
2240.2.k.f 16
2240.2.k.g 16
2240.2.l \(\chi_{2240}(1569, \cdot)\) 2240.2.l.a 12 1
2240.2.l.b 12
2240.2.l.c 24
2240.2.l.d 24
2240.2.n \(\chi_{2240}(1119, \cdot)\) 2240.2.n.a 8 1
2240.2.n.b 8
2240.2.n.c 8
2240.2.n.d 8
2240.2.n.e 8
2240.2.n.f 8
2240.2.n.g 8
2240.2.n.h 8
2240.2.n.i 16
2240.2.n.j 16
2240.2.q \(\chi_{2240}(641, \cdot)\) n/a 128 2
2240.2.r \(\chi_{2240}(433, \cdot)\) n/a 184 2
2240.2.t \(\chi_{2240}(463, \cdot)\) n/a 144 2
2240.2.w \(\chi_{2240}(97, \cdot)\) n/a 192 2
2240.2.x \(\chi_{2240}(127, \cdot)\) n/a 144 2
2240.2.bb \(\chi_{2240}(1009, \cdot)\) n/a 144 2
2240.2.bc \(\chi_{2240}(111, \cdot)\) n/a 128 2
2240.2.bd \(\chi_{2240}(561, \cdot)\) 2240.2.bd.a 44 2
2240.2.bd.b 52
2240.2.be \(\chi_{2240}(559, \cdot)\) n/a 184 2
2240.2.bi \(\chi_{2240}(1247, \cdot)\) n/a 144 2
2240.2.bj \(\chi_{2240}(1217, \cdot)\) n/a 184 2
2240.2.bl \(\chi_{2240}(1583, \cdot)\) n/a 144 2
2240.2.bn \(\chi_{2240}(1553, \cdot)\) n/a 184 2
2240.2.bq \(\chi_{2240}(159, \cdot)\) n/a 192 2
2240.2.bs \(\chi_{2240}(831, \cdot)\) n/a 128 2
2240.2.bv \(\chi_{2240}(289, \cdot)\) n/a 192 2
2240.2.bw \(\chi_{2240}(1089, \cdot)\) n/a 184 2
2240.2.bz \(\chi_{2240}(31, \cdot)\) n/a 128 2
2240.2.cb \(\chi_{2240}(1761, \cdot)\) n/a 128 2
2240.2.cc \(\chi_{2240}(1279, \cdot)\) n/a 184 2
2240.2.cg \(\chi_{2240}(281, \cdot)\) None 0 4
2240.2.ch \(\chi_{2240}(279, \cdot)\) None 0 4
2240.2.ci \(\chi_{2240}(377, \cdot)\) None 0 4
2240.2.cj \(\chi_{2240}(407, \cdot)\) None 0 4
2240.2.cm \(\chi_{2240}(183, \cdot)\) None 0 4
2240.2.cn \(\chi_{2240}(153, \cdot)\) None 0 4
2240.2.cs \(\chi_{2240}(391, \cdot)\) None 0 4
2240.2.ct \(\chi_{2240}(169, \cdot)\) None 0 4
2240.2.cv \(\chi_{2240}(207, \cdot)\) n/a 368 4
2240.2.cx \(\chi_{2240}(593, \cdot)\) n/a 368 4
2240.2.cy \(\chi_{2240}(257, \cdot)\) n/a 368 4
2240.2.db \(\chi_{2240}(543, \cdot)\) n/a 384 4
2240.2.de \(\chi_{2240}(719, \cdot)\) n/a 368 4
2240.2.df \(\chi_{2240}(81, \cdot)\) n/a 256 4
2240.2.dg \(\chi_{2240}(271, \cdot)\) n/a 256 4
2240.2.dh \(\chi_{2240}(529, \cdot)\) n/a 368 4
2240.2.dk \(\chi_{2240}(767, \cdot)\) n/a 368 4
2240.2.dn \(\chi_{2240}(33, \cdot)\) n/a 384 4
2240.2.dp \(\chi_{2240}(17, \cdot)\) n/a 368 4
2240.2.dr \(\chi_{2240}(1103, \cdot)\) n/a 368 4
2240.2.du \(\chi_{2240}(13, \cdot)\) n/a 3040 8
2240.2.dv \(\chi_{2240}(43, \cdot)\) n/a 2304 8
2240.2.dw \(\chi_{2240}(139, \cdot)\) n/a 3040 8
2240.2.dx \(\chi_{2240}(141, \cdot)\) n/a 1536 8
2240.2.dy \(\chi_{2240}(251, \cdot)\) n/a 2048 8
2240.2.dz \(\chi_{2240}(29, \cdot)\) n/a 2304 8
2240.2.eg \(\chi_{2240}(267, \cdot)\) n/a 2304 8
2240.2.eh \(\chi_{2240}(237, \cdot)\) n/a 3040 8
2240.2.ei \(\chi_{2240}(9, \cdot)\) None 0 8
2240.2.ej \(\chi_{2240}(311, \cdot)\) None 0 8
2240.2.eo \(\chi_{2240}(23, \cdot)\) None 0 8
2240.2.ep \(\chi_{2240}(297, \cdot)\) None 0 8
2240.2.es \(\chi_{2240}(73, \cdot)\) None 0 8
2240.2.et \(\chi_{2240}(247, \cdot)\) None 0 8
2240.2.eu \(\chi_{2240}(199, \cdot)\) None 0 8
2240.2.ev \(\chi_{2240}(121, \cdot)\) None 0 8
2240.2.ey \(\chi_{2240}(157, \cdot)\) n/a 6080 16
2240.2.ez \(\chi_{2240}(107, \cdot)\) n/a 6080 16
2240.2.fg \(\chi_{2240}(109, \cdot)\) n/a 6080 16
2240.2.fh \(\chi_{2240}(131, \cdot)\) n/a 4096 16
2240.2.fi \(\chi_{2240}(221, \cdot)\) n/a 4096 16
2240.2.fj \(\chi_{2240}(19, \cdot)\) n/a 6080 16
2240.2.fk \(\chi_{2240}(67, \cdot)\) n/a 6080 16
2240.2.fl \(\chi_{2240}(117, \cdot)\) n/a 6080 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2240))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2240)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2240))\)\(^{\oplus 1}\)