Properties

Label 2400.2
Level 2400
Weight 2
Dimension 59314
Nonzero newspaces 40
Sturm bound 614400
Trace bound 25

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Defining parameters

Level: \( N \) = \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(614400\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2400))\).

Total New Old
Modular forms 157184 60134 97050
Cusp forms 150017 59314 90703
Eisenstein series 7167 820 6347

Trace form

\( 59314q - 38q^{3} - 104q^{4} - 84q^{6} - 76q^{7} - 74q^{9} + O(q^{10}) \) \( 59314q - 38q^{3} - 104q^{4} - 84q^{6} - 76q^{7} - 74q^{9} - 128q^{10} - 68q^{12} - 116q^{13} - 32q^{14} - 48q^{15} - 208q^{16} - 16q^{17} - 60q^{18} - 100q^{19} - 100q^{21} - 128q^{22} - 24q^{23} - 40q^{24} - 192q^{25} + 40q^{26} - 74q^{27} - 64q^{28} - 28q^{29} - 64q^{30} - 236q^{31} + 40q^{32} - 192q^{33} - 80q^{34} - 48q^{35} - 32q^{36} - 244q^{37} + 40q^{38} - 112q^{39} - 128q^{40} - 120q^{41} + 8q^{42} - 204q^{43} + 8q^{44} - 80q^{45} - 168q^{46} - 72q^{47} - 138q^{49} - 136q^{51} - 56q^{52} - 44q^{53} - 136q^{55} + 56q^{56} - 8q^{57} - 32q^{58} + 64q^{59} - 228q^{61} + 48q^{62} + 32q^{63} + 160q^{64} + 64q^{65} + 196q^{66} + 68q^{67} + 440q^{68} + 76q^{69} + 160q^{70} + 168q^{71} + 368q^{72} + 60q^{73} + 672q^{74} + 8q^{75} + 184q^{76} + 320q^{77} + 492q^{78} + 164q^{79} + 320q^{80} + 178q^{81} + 456q^{82} + 160q^{83} + 424q^{84} + 64q^{85} + 448q^{86} + 164q^{87} + 512q^{88} + 256q^{89} + 176q^{90} + 496q^{92} + 152q^{93} + 256q^{94} + 48q^{95} + 32q^{96} - 140q^{97} + 112q^{98} + 196q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2400))\)

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
2400.2.a \(\chi_{2400}(1, \cdot)\) 2400.2.a.a 1 1
2400.2.a.b 1
2400.2.a.c 1
2400.2.a.d 1
2400.2.a.e 1
2400.2.a.f 1
2400.2.a.g 1
2400.2.a.h 1
2400.2.a.i 1
2400.2.a.j 1
2400.2.a.k 1
2400.2.a.l 1
2400.2.a.m 1
2400.2.a.n 1
2400.2.a.o 1
2400.2.a.p 1
2400.2.a.q 1
2400.2.a.r 1
2400.2.a.s 1
2400.2.a.t 1
2400.2.a.u 1
2400.2.a.v 1
2400.2.a.w 1
2400.2.a.x 1
2400.2.a.y 1
2400.2.a.z 1
2400.2.a.ba 1
2400.2.a.bb 1
2400.2.a.bc 1
2400.2.a.bd 1
2400.2.a.be 1
2400.2.a.bf 1
2400.2.a.bg 1
2400.2.a.bh 1
2400.2.a.bi 2
2400.2.a.bj 2
2400.2.b \(\chi_{2400}(2351, \cdot)\) 2400.2.b.a 2 1
2400.2.b.b 4
2400.2.b.c 4
2400.2.b.d 4
2400.2.b.e 8
2400.2.b.f 8
2400.2.b.g 12
2400.2.b.h 12
2400.2.b.i 16
2400.2.d \(\chi_{2400}(49, \cdot)\) 2400.2.d.a 2 1
2400.2.d.b 2
2400.2.d.c 2
2400.2.d.d 2
2400.2.d.e 6
2400.2.d.f 6
2400.2.d.g 8
2400.2.d.h 8
2400.2.f \(\chi_{2400}(1249, \cdot)\) 2400.2.f.a 2 1
2400.2.f.b 2
2400.2.f.c 2
2400.2.f.d 2
2400.2.f.e 2
2400.2.f.f 2
2400.2.f.g 2
2400.2.f.h 2
2400.2.f.i 2
2400.2.f.j 2
2400.2.f.k 2
2400.2.f.l 2
2400.2.f.m 2
2400.2.f.n 2
2400.2.f.o 2
2400.2.f.p 2
2400.2.f.q 2
2400.2.f.r 2
2400.2.h \(\chi_{2400}(1151, \cdot)\) 2400.2.h.a 4 1
2400.2.h.b 4
2400.2.h.c 4
2400.2.h.d 4
2400.2.h.e 4
2400.2.h.f 16
2400.2.h.g 16
2400.2.h.h 24
2400.2.k \(\chi_{2400}(1201, \cdot)\) 2400.2.k.a 2 1
2400.2.k.b 2
2400.2.k.c 6
2400.2.k.d 8
2400.2.k.e 8
2400.2.k.f 12
2400.2.m \(\chi_{2400}(1199, \cdot)\) 2400.2.m.a 4 1
2400.2.m.b 8
2400.2.m.c 16
2400.2.m.d 16
2400.2.m.e 24
2400.2.o \(\chi_{2400}(2399, \cdot)\) 2400.2.o.a 4 1
2400.2.o.b 4
2400.2.o.c 4
2400.2.o.d 4
2400.2.o.e 4
2400.2.o.f 4
2400.2.o.g 4
2400.2.o.h 4
2400.2.o.i 4
2400.2.o.j 4
2400.2.o.k 16
2400.2.o.l 16
2400.2.s \(\chi_{2400}(601, \cdot)\) None 0 2
2400.2.t \(\chi_{2400}(599, \cdot)\) None 0 2
2400.2.v \(\chi_{2400}(257, \cdot)\) n/a 144 2
2400.2.w \(\chi_{2400}(607, \cdot)\) 2400.2.w.a 4 2
2400.2.w.b 4
2400.2.w.c 4
2400.2.w.d 4
2400.2.w.e 4
2400.2.w.f 4
2400.2.w.g 8
2400.2.w.h 8
2400.2.w.i 8
2400.2.w.j 8
2400.2.w.k 8
2400.2.w.l 8
2400.2.y \(\chi_{2400}(7, \cdot)\) None 0 2
2400.2.bb \(\chi_{2400}(857, \cdot)\) None 0 2
2400.2.bc \(\chi_{2400}(1207, \cdot)\) None 0 2
2400.2.bf \(\chi_{2400}(2057, \cdot)\) None 0 2
2400.2.bh \(\chi_{2400}(943, \cdot)\) 2400.2.bh.a 16 2
2400.2.bh.b 24
2400.2.bh.c 32
2400.2.bi \(\chi_{2400}(593, \cdot)\) n/a 136 2
2400.2.bk \(\chi_{2400}(551, \cdot)\) None 0 2
2400.2.bl \(\chi_{2400}(649, \cdot)\) None 0 2
2400.2.bo \(\chi_{2400}(481, \cdot)\) n/a 240 4
2400.2.bp \(\chi_{2400}(43, \cdot)\) n/a 576 4
2400.2.bs \(\chi_{2400}(893, \cdot)\) n/a 1136 4
2400.2.bt \(\chi_{2400}(299, \cdot)\) n/a 1136 4
2400.2.bw \(\chi_{2400}(301, \cdot)\) n/a 608 4
2400.2.by \(\chi_{2400}(251, \cdot)\) n/a 1192 4
2400.2.bz \(\chi_{2400}(349, \cdot)\) n/a 576 4
2400.2.cc \(\chi_{2400}(293, \cdot)\) n/a 1136 4
2400.2.cd \(\chi_{2400}(643, \cdot)\) n/a 576 4
2400.2.cg \(\chi_{2400}(191, \cdot)\) n/a 480 4
2400.2.ci \(\chi_{2400}(289, \cdot)\) n/a 240 4
2400.2.ck \(\chi_{2400}(529, \cdot)\) n/a 240 4
2400.2.cm \(\chi_{2400}(431, \cdot)\) n/a 464 4
2400.2.co \(\chi_{2400}(479, \cdot)\) n/a 480 4
2400.2.cq \(\chi_{2400}(239, \cdot)\) n/a 464 4
2400.2.cs \(\chi_{2400}(241, \cdot)\) n/a 240 4
2400.2.cu \(\chi_{2400}(119, \cdot)\) None 0 8
2400.2.cv \(\chi_{2400}(121, \cdot)\) None 0 8
2400.2.cz \(\chi_{2400}(17, \cdot)\) n/a 928 8
2400.2.da \(\chi_{2400}(367, \cdot)\) n/a 480 8
2400.2.dc \(\chi_{2400}(137, \cdot)\) None 0 8
2400.2.df \(\chi_{2400}(103, \cdot)\) None 0 8
2400.2.dg \(\chi_{2400}(233, \cdot)\) None 0 8
2400.2.dj \(\chi_{2400}(487, \cdot)\) None 0 8
2400.2.dl \(\chi_{2400}(127, \cdot)\) n/a 480 8
2400.2.dm \(\chi_{2400}(353, \cdot)\) n/a 960 8
2400.2.dq \(\chi_{2400}(169, \cdot)\) None 0 8
2400.2.dr \(\chi_{2400}(71, \cdot)\) None 0 8
2400.2.ds \(\chi_{2400}(173, \cdot)\) n/a 7616 16
2400.2.dv \(\chi_{2400}(67, \cdot)\) n/a 3840 16
2400.2.dx \(\chi_{2400}(109, \cdot)\) n/a 3840 16
2400.2.dy \(\chi_{2400}(11, \cdot)\) n/a 7616 16
2400.2.ea \(\chi_{2400}(61, \cdot)\) n/a 3840 16
2400.2.ed \(\chi_{2400}(59, \cdot)\) n/a 7616 16
2400.2.ef \(\chi_{2400}(163, \cdot)\) n/a 3840 16
2400.2.eg \(\chi_{2400}(53, \cdot)\) n/a 7616 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2400))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2400)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 2}\)