Properties

Label 1120.2
Level 1120
Weight 2
Dimension 17916
Nonzero newspaces 40
Sturm bound 147456
Trace bound 21

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Defining parameters

Level: \( N \) = \( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(147456\)
Trace bound: \(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1120))\).

Total New Old
Modular forms 38400 18516 19884
Cusp forms 35329 17916 17413
Eisenstein series 3071 600 2471

Trace form

\( 17916q - 32q^{2} - 28q^{3} - 32q^{4} - 52q^{5} - 96q^{6} - 32q^{7} - 80q^{8} - 52q^{9} + O(q^{10}) \) \( 17916q - 32q^{2} - 28q^{3} - 32q^{4} - 52q^{5} - 96q^{6} - 32q^{7} - 80q^{8} - 52q^{9} - 32q^{10} - 76q^{11} + 32q^{12} - 8q^{13} - 8q^{14} - 84q^{15} - 16q^{16} + 48q^{18} - 20q^{19} - 16q^{20} - 120q^{21} - 32q^{22} + 4q^{23} - 80q^{24} - 80q^{25} - 176q^{26} + 104q^{27} - 80q^{28} - 104q^{29} - 112q^{30} + 36q^{31} - 112q^{32} - 8q^{33} - 80q^{34} + 2q^{35} - 352q^{36} + 40q^{37} + 160q^{39} - 24q^{40} - 32q^{41} + 56q^{43} + 128q^{44} + 116q^{45} + 32q^{46} + 108q^{47} + 176q^{48} + 84q^{49} - 40q^{50} + 60q^{51} + 200q^{53} + 16q^{54} - 20q^{55} - 96q^{56} + 32q^{57} - 48q^{58} - 52q^{59} - 184q^{60} + 88q^{61} - 112q^{62} - 16q^{63} - 320q^{64} - 156q^{65} - 448q^{66} - 164q^{67} - 176q^{68} - 216q^{70} - 352q^{71} - 416q^{72} - 192q^{73} - 320q^{74} - 214q^{75} - 352q^{76} - 104q^{77} - 528q^{78} - 132q^{79} - 376q^{80} - 332q^{81} - 352q^{82} + 64q^{83} - 304q^{84} - 280q^{85} - 432q^{86} + 144q^{87} - 368q^{88} - 128q^{89} - 648q^{90} - 112q^{91} - 560q^{92} - 368q^{93} - 496q^{94} + 38q^{95} - 816q^{96} - 256q^{97} - 464q^{98} + 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1120))\)

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
1120.2.a \(\chi_{1120}(1, \cdot)\) 1120.2.a.a 1 1
1120.2.a.b 1
1120.2.a.c 1
1120.2.a.d 1
1120.2.a.e 1
1120.2.a.f 1
1120.2.a.g 1
1120.2.a.h 1
1120.2.a.i 1
1120.2.a.j 1
1120.2.a.k 1
1120.2.a.l 1
1120.2.a.m 1
1120.2.a.n 1
1120.2.a.o 1
1120.2.a.p 1
1120.2.a.q 2
1120.2.a.r 2
1120.2.a.s 2
1120.2.a.t 2
1120.2.b \(\chi_{1120}(561, \cdot)\) 1120.2.b.a 2 1
1120.2.b.b 2
1120.2.b.c 8
1120.2.b.d 12
1120.2.e \(\chi_{1120}(1119, \cdot)\) 1120.2.e.a 48 1
1120.2.g \(\chi_{1120}(449, \cdot)\) 1120.2.g.a 4 1
1120.2.g.b 10
1120.2.g.c 10
1120.2.g.d 12
1120.2.h \(\chi_{1120}(111, \cdot)\) 1120.2.h.a 16 1
1120.2.h.b 16
1120.2.k \(\chi_{1120}(671, \cdot)\) 1120.2.k.a 16 1
1120.2.k.b 16
1120.2.l \(\chi_{1120}(1009, \cdot)\) 1120.2.l.a 36 1
1120.2.n \(\chi_{1120}(559, \cdot)\) 1120.2.n.a 4 1
1120.2.n.b 40
1120.2.q \(\chi_{1120}(641, \cdot)\) 1120.2.q.a 2 2
1120.2.q.b 2
1120.2.q.c 2
1120.2.q.d 2
1120.2.q.e 4
1120.2.q.f 4
1120.2.q.g 8
1120.2.q.h 8
1120.2.q.i 10
1120.2.q.j 10
1120.2.q.k 12
1120.2.r \(\chi_{1120}(153, \cdot)\) None 0 2
1120.2.t \(\chi_{1120}(407, \cdot)\) None 0 2
1120.2.w \(\chi_{1120}(433, \cdot)\) 1120.2.w.a 8 2
1120.2.w.b 8
1120.2.w.c 72
1120.2.x \(\chi_{1120}(127, \cdot)\) 1120.2.x.a 4 2
1120.2.x.b 4
1120.2.x.c 12
1120.2.x.d 12
1120.2.x.e 20
1120.2.x.f 20
1120.2.bb \(\chi_{1120}(169, \cdot)\) None 0 2
1120.2.bc \(\chi_{1120}(391, \cdot)\) None 0 2
1120.2.bd \(\chi_{1120}(281, \cdot)\) None 0 2
1120.2.be \(\chi_{1120}(279, \cdot)\) None 0 2
1120.2.bi \(\chi_{1120}(463, \cdot)\) 1120.2.bi.a 72 2
1120.2.bj \(\chi_{1120}(97, \cdot)\) 1120.2.bj.a 8 2
1120.2.bj.b 8
1120.2.bj.c 32
1120.2.bj.d 48
1120.2.bl \(\chi_{1120}(183, \cdot)\) None 0 2
1120.2.bn \(\chi_{1120}(377, \cdot)\) None 0 2
1120.2.bq \(\chi_{1120}(719, \cdot)\) 1120.2.bq.a 8 2
1120.2.bq.b 80
1120.2.bs \(\chi_{1120}(31, \cdot)\) 1120.2.bs.a 32 2
1120.2.bs.b 32
1120.2.bv \(\chi_{1120}(529, \cdot)\) 1120.2.bv.a 88 2
1120.2.bw \(\chi_{1120}(289, \cdot)\) 1120.2.bw.a 4 2
1120.2.bw.b 4
1120.2.bw.c 8
1120.2.bw.d 8
1120.2.bw.e 8
1120.2.bw.f 8
1120.2.bw.g 16
1120.2.bw.h 40
1120.2.bz \(\chi_{1120}(271, \cdot)\) 1120.2.bz.a 4 2
1120.2.bz.b 4
1120.2.bz.c 4
1120.2.bz.d 4
1120.2.bz.e 24
1120.2.bz.f 24
1120.2.cb \(\chi_{1120}(81, \cdot)\) 1120.2.cb.a 4 2
1120.2.cb.b 60
1120.2.cc \(\chi_{1120}(159, \cdot)\) 1120.2.cc.a 8 2
1120.2.cc.b 8
1120.2.cc.c 80
1120.2.cg \(\chi_{1120}(141, \cdot)\) n/a 384 4
1120.2.ch \(\chi_{1120}(139, \cdot)\) n/a 752 4
1120.2.ci \(\chi_{1120}(13, \cdot)\) n/a 752 4
1120.2.cj \(\chi_{1120}(43, \cdot)\) n/a 576 4
1120.2.cm \(\chi_{1120}(267, \cdot)\) n/a 576 4
1120.2.cn \(\chi_{1120}(237, \cdot)\) n/a 752 4
1120.2.cs \(\chi_{1120}(251, \cdot)\) n/a 512 4
1120.2.ct \(\chi_{1120}(29, \cdot)\) n/a 576 4
1120.2.cv \(\chi_{1120}(23, \cdot)\) None 0 4
1120.2.cx \(\chi_{1120}(73, \cdot)\) None 0 4
1120.2.cy \(\chi_{1120}(33, \cdot)\) n/a 192 4
1120.2.db \(\chi_{1120}(207, \cdot)\) n/a 176 4
1120.2.de \(\chi_{1120}(199, \cdot)\) None 0 4
1120.2.df \(\chi_{1120}(121, \cdot)\) None 0 4
1120.2.dg \(\chi_{1120}(311, \cdot)\) None 0 4
1120.2.dh \(\chi_{1120}(9, \cdot)\) None 0 4
1120.2.dk \(\chi_{1120}(543, \cdot)\) n/a 192 4
1120.2.dn \(\chi_{1120}(17, \cdot)\) n/a 176 4
1120.2.dp \(\chi_{1120}(297, \cdot)\) None 0 4
1120.2.dr \(\chi_{1120}(247, \cdot)\) None 0 4
1120.2.ds \(\chi_{1120}(109, \cdot)\) n/a 1504 8
1120.2.dt \(\chi_{1120}(131, \cdot)\) n/a 1024 8
1120.2.dy \(\chi_{1120}(107, \cdot)\) n/a 1504 8
1120.2.dz \(\chi_{1120}(157, \cdot)\) n/a 1504 8
1120.2.ec \(\chi_{1120}(117, \cdot)\) n/a 1504 8
1120.2.ed \(\chi_{1120}(67, \cdot)\) n/a 1504 8
1120.2.ee \(\chi_{1120}(19, \cdot)\) n/a 1504 8
1120.2.ef \(\chi_{1120}(221, \cdot)\) n/a 1024 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1120))\) into lower level spaces

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