Properties

Label 1440.2
Level 1440
Weight 2
Dimension 22302
Nonzero newspaces 40
Sturm bound 221184
Trace bound 53

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Defining parameters

Level: \( N \) = \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(221184\)
Trace bound: \(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1440))\).

Total New Old
Modular forms 57344 22842 34502
Cusp forms 53249 22302 30947
Eisenstein series 4095 540 3555

Trace form

\( 22302q - 24q^{2} - 24q^{3} - 24q^{4} - 34q^{5} - 96q^{6} - 16q^{7} - 24q^{8} - 48q^{9} + O(q^{10}) \) \( 22302q - 24q^{2} - 24q^{3} - 24q^{4} - 34q^{5} - 96q^{6} - 16q^{7} - 24q^{8} - 48q^{9} - 116q^{10} - 60q^{11} - 32q^{12} - 36q^{13} - 56q^{14} - 42q^{15} - 112q^{16} - 52q^{17} - 32q^{18} - 88q^{19} - 52q^{20} - 128q^{21} - 48q^{22} - 72q^{23} - 32q^{24} - 82q^{25} - 32q^{26} - 48q^{27} - 32q^{28} - 76q^{29} - 32q^{30} - 140q^{31} + 16q^{32} - 72q^{33} - 72q^{35} - 48q^{36} - 44q^{37} + 184q^{38} - 12q^{39} + 80q^{40} - 36q^{41} + 128q^{42} + 248q^{44} - 24q^{46} + 72q^{47} + 176q^{48} + 94q^{49} + 132q^{50} - 8q^{51} + 216q^{52} + 100q^{53} + 144q^{54} - 56q^{55} + 224q^{56} + 48q^{57} + 240q^{58} + 124q^{59} + 8q^{60} - 84q^{61} + 48q^{62} + 84q^{63} + 48q^{64} + 24q^{65} - 96q^{66} + 56q^{67} + 176q^{68} + 96q^{69} + 120q^{70} + 96q^{71} - 32q^{72} - 132q^{73} + 120q^{74} + 26q^{75} + 56q^{76} + 104q^{77} - 80q^{78} + 164q^{79} + 112q^{81} - 232q^{82} + 376q^{83} - 256q^{84} + 28q^{85} - 320q^{86} + 316q^{87} - 176q^{88} + 148q^{89} - 192q^{90} + 200q^{91} - 416q^{92} - 32q^{93} - 256q^{94} + 296q^{95} - 368q^{96} + 60q^{97} - 416q^{98} + 332q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1440))\)

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
1440.2.a \(\chi_{1440}(1, \cdot)\) 1440.2.a.a 1 1
1440.2.a.b 1
1440.2.a.c 1
1440.2.a.d 1
1440.2.a.e 1
1440.2.a.f 1
1440.2.a.g 1
1440.2.a.h 1
1440.2.a.i 1
1440.2.a.j 1
1440.2.a.k 1
1440.2.a.l 1
1440.2.a.m 1
1440.2.a.n 1
1440.2.a.o 2
1440.2.a.p 2
1440.2.a.q 2
1440.2.b \(\chi_{1440}(431, \cdot)\) 1440.2.b.a 2 1
1440.2.b.b 2
1440.2.b.c 6
1440.2.b.d 6
1440.2.d \(\chi_{1440}(1009, \cdot)\) 1440.2.d.a 4 1
1440.2.d.b 4
1440.2.d.c 4
1440.2.d.d 4
1440.2.d.e 6
1440.2.d.f 6
1440.2.f \(\chi_{1440}(289, \cdot)\) 1440.2.f.a 2 1
1440.2.f.b 2
1440.2.f.c 2
1440.2.f.d 2
1440.2.f.e 2
1440.2.f.f 2
1440.2.f.g 2
1440.2.f.h 4
1440.2.f.i 4
1440.2.f.j 8
1440.2.h \(\chi_{1440}(1151, \cdot)\) 1440.2.h.a 4 1
1440.2.h.b 4
1440.2.h.c 4
1440.2.h.d 4
1440.2.k \(\chi_{1440}(721, \cdot)\) 1440.2.k.a 2 1
1440.2.k.b 2
1440.2.k.c 2
1440.2.k.d 4
1440.2.k.e 4
1440.2.k.f 6
1440.2.m \(\chi_{1440}(719, \cdot)\) 1440.2.m.a 4 1
1440.2.m.b 4
1440.2.m.c 16
1440.2.o \(\chi_{1440}(1439, \cdot)\) 1440.2.o.a 12 1
1440.2.o.b 12
1440.2.q \(\chi_{1440}(481, \cdot)\) 1440.2.q.a 2 2
1440.2.q.b 2
1440.2.q.c 2
1440.2.q.d 2
1440.2.q.e 2
1440.2.q.f 2
1440.2.q.g 2
1440.2.q.h 2
1440.2.q.i 8
1440.2.q.j 8
1440.2.q.k 8
1440.2.q.l 8
1440.2.q.m 8
1440.2.q.n 8
1440.2.q.o 10
1440.2.q.p 10
1440.2.q.q 12
1440.2.t \(\chi_{1440}(361, \cdot)\) None 0 2
1440.2.u \(\chi_{1440}(359, \cdot)\) None 0 2
1440.2.w \(\chi_{1440}(737, \cdot)\) 1440.2.w.a 4 2
1440.2.w.b 4
1440.2.w.c 4
1440.2.w.d 4
1440.2.w.e 8
1440.2.w.f 12
1440.2.w.g 12
1440.2.x \(\chi_{1440}(127, \cdot)\) 1440.2.x.a 2 2
1440.2.x.b 2
1440.2.x.c 2
1440.2.x.d 2
1440.2.x.e 2
1440.2.x.f 2
1440.2.x.g 2
1440.2.x.h 2
1440.2.x.i 2
1440.2.x.j 2
1440.2.x.k 4
1440.2.x.l 4
1440.2.x.m 4
1440.2.x.n 4
1440.2.x.o 4
1440.2.x.p 4
1440.2.x.q 8
1440.2.x.r 8
1440.2.z \(\chi_{1440}(343, \cdot)\) None 0 2
1440.2.bc \(\chi_{1440}(233, \cdot)\) None 0 2
1440.2.bd \(\chi_{1440}(1063, \cdot)\) None 0 2
1440.2.bg \(\chi_{1440}(953, \cdot)\) None 0 2
1440.2.bi \(\chi_{1440}(847, \cdot)\) 1440.2.bi.a 4 2
1440.2.bi.b 4
1440.2.bi.c 8
1440.2.bi.d 16
1440.2.bi.e 24
1440.2.bj \(\chi_{1440}(17, \cdot)\) 1440.2.bj.a 48 2
1440.2.bl \(\chi_{1440}(71, \cdot)\) None 0 2
1440.2.bm \(\chi_{1440}(649, \cdot)\) None 0 2
1440.2.br \(\chi_{1440}(479, \cdot)\) n/a 144 2
1440.2.bt \(\chi_{1440}(239, \cdot)\) n/a 136 2
1440.2.bv \(\chi_{1440}(241, \cdot)\) 1440.2.bv.a 4 2
1440.2.bv.b 92
1440.2.bw \(\chi_{1440}(191, \cdot)\) 1440.2.bw.a 48 2
1440.2.bw.b 48
1440.2.by \(\chi_{1440}(769, \cdot)\) n/a 144 2
1440.2.ca \(\chi_{1440}(49, \cdot)\) n/a 136 2
1440.2.cc \(\chi_{1440}(911, \cdot)\) 1440.2.cc.a 48 2
1440.2.cc.b 48
1440.2.ce \(\chi_{1440}(307, \cdot)\) n/a 472 4
1440.2.ch \(\chi_{1440}(197, \cdot)\) n/a 384 4
1440.2.ci \(\chi_{1440}(179, \cdot)\) n/a 384 4
1440.2.cl \(\chi_{1440}(181, \cdot)\) n/a 320 4
1440.2.cn \(\chi_{1440}(251, \cdot)\) n/a 256 4
1440.2.co \(\chi_{1440}(109, \cdot)\) n/a 472 4
1440.2.cr \(\chi_{1440}(53, \cdot)\) n/a 384 4
1440.2.cs \(\chi_{1440}(163, \cdot)\) n/a 472 4
1440.2.cu \(\chi_{1440}(169, \cdot)\) None 0 4
1440.2.cv \(\chi_{1440}(311, \cdot)\) None 0 4
1440.2.cy \(\chi_{1440}(367, \cdot)\) n/a 272 4
1440.2.db \(\chi_{1440}(113, \cdot)\) n/a 272 4
1440.2.dc \(\chi_{1440}(137, \cdot)\) None 0 4
1440.2.df \(\chi_{1440}(103, \cdot)\) None 0 4
1440.2.dg \(\chi_{1440}(713, \cdot)\) None 0 4
1440.2.dj \(\chi_{1440}(7, \cdot)\) None 0 4
1440.2.dk \(\chi_{1440}(257, \cdot)\) n/a 288 4
1440.2.dn \(\chi_{1440}(223, \cdot)\) n/a 288 4
1440.2.dq \(\chi_{1440}(119, \cdot)\) None 0 4
1440.2.dr \(\chi_{1440}(121, \cdot)\) None 0 4
1440.2.dt \(\chi_{1440}(187, \cdot)\) n/a 2272 8
1440.2.du \(\chi_{1440}(77, \cdot)\) n/a 2272 8
1440.2.dw \(\chi_{1440}(61, \cdot)\) n/a 1536 8
1440.2.dz \(\chi_{1440}(59, \cdot)\) n/a 2272 8
1440.2.eb \(\chi_{1440}(229, \cdot)\) n/a 2272 8
1440.2.ec \(\chi_{1440}(11, \cdot)\) n/a 1536 8
1440.2.ee \(\chi_{1440}(173, \cdot)\) n/a 2272 8
1440.2.eh \(\chi_{1440}(43, \cdot)\) n/a 2272 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1440))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1440)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 2}\)