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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

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

Display 100 coefficients 10 coefficients

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 available 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

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