Properties

Label 560.2
Level 560
Weight 2
Dimension 4418
Nonzero newspaces 28
Newform subspaces 89
Sturm bound 36864
Trace bound 11

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Defining parameters

Level: \( N \) = \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 28 \)
Newform subspaces: \( 89 \)
Sturm bound: \(36864\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(560))\).

Total New Old
Modular forms 9888 4690 5198
Cusp forms 8545 4418 4127
Eisenstein series 1343 272 1071

Trace form

\( 4418q - 16q^{2} - 14q^{3} - 8q^{4} - 29q^{5} - 24q^{6} - 12q^{7} - 16q^{8} + 2q^{9} + O(q^{10}) \) \( 4418q - 16q^{2} - 14q^{3} - 8q^{4} - 29q^{5} - 24q^{6} - 12q^{7} - 16q^{8} + 2q^{9} - 20q^{10} - 22q^{11} - 24q^{12} - 4q^{13} - 24q^{14} - 10q^{15} - 72q^{16} - 18q^{17} + 50q^{19} - 12q^{20} - 22q^{21} - 32q^{22} + 54q^{23} - 8q^{24} + 35q^{25} - 24q^{26} + 16q^{27} - 32q^{28} + 4q^{29} - 92q^{30} - 62q^{31} - 56q^{32} - 38q^{33} - 120q^{34} - 19q^{35} - 256q^{36} - 42q^{37} - 168q^{38} - 64q^{39} - 196q^{40} - 68q^{41} - 240q^{42} - 28q^{43} - 232q^{44} - 120q^{45} - 240q^{46} + 22q^{47} - 344q^{48} - 106q^{49} - 192q^{50} - 42q^{51} - 304q^{52} - 114q^{53} - 440q^{54} - 26q^{55} - 240q^{56} - 124q^{57} - 224q^{58} - 10q^{59} - 124q^{60} - 186q^{61} - 160q^{62} - 104q^{63} - 152q^{64} - 14q^{65} - 136q^{66} - 142q^{67} - 16q^{68} - 108q^{69} + 4q^{70} - 136q^{71} + 56q^{72} + 86q^{73} + 168q^{74} - 185q^{75} + 136q^{76} + 74q^{77} + 224q^{78} - 110q^{79} + 156q^{80} + 68q^{81} + 120q^{82} - 88q^{83} + 120q^{84} - 22q^{85} + 88q^{86} - 160q^{87} + 200q^{88} + 138q^{89} + 284q^{90} - 192q^{91} - 24q^{92} + 154q^{93} + 184q^{94} - 167q^{95} + 264q^{96} + 76q^{97} + 136q^{98} - 408q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(560))\)

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
560.2.a \(\chi_{560}(1, \cdot)\) 560.2.a.a 1 1
560.2.a.b 1
560.2.a.c 1
560.2.a.d 1
560.2.a.e 1
560.2.a.f 1
560.2.a.g 2
560.2.a.h 2
560.2.a.i 2
560.2.b \(\chi_{560}(281, \cdot)\) None 0 1
560.2.e \(\chi_{560}(559, \cdot)\) 560.2.e.a 4 1
560.2.e.b 4
560.2.e.c 8
560.2.e.d 8
560.2.g \(\chi_{560}(449, \cdot)\) 560.2.g.a 2 1
560.2.g.b 2
560.2.g.c 2
560.2.g.d 2
560.2.g.e 4
560.2.g.f 6
560.2.h \(\chi_{560}(391, \cdot)\) None 0 1
560.2.k \(\chi_{560}(111, \cdot)\) 560.2.k.a 8 1
560.2.k.b 8
560.2.l \(\chi_{560}(169, \cdot)\) None 0 1
560.2.n \(\chi_{560}(279, \cdot)\) None 0 1
560.2.q \(\chi_{560}(81, \cdot)\) 560.2.q.a 2 2
560.2.q.b 2
560.2.q.c 2
560.2.q.d 2
560.2.q.e 2
560.2.q.f 2
560.2.q.g 2
560.2.q.h 2
560.2.q.i 2
560.2.q.j 4
560.2.q.k 4
560.2.q.l 6
560.2.r \(\chi_{560}(237, \cdot)\) 560.2.r.a 184 2
560.2.t \(\chi_{560}(43, \cdot)\) 560.2.t.a 144 2
560.2.w \(\chi_{560}(153, \cdot)\) None 0 2
560.2.x \(\chi_{560}(127, \cdot)\) 560.2.x.a 12 2
560.2.x.b 24
560.2.bb \(\chi_{560}(29, \cdot)\) 560.2.bb.a 2 2
560.2.bb.b 2
560.2.bb.c 70
560.2.bb.d 70
560.2.bc \(\chi_{560}(251, \cdot)\) 560.2.bc.a 128 2
560.2.bd \(\chi_{560}(141, \cdot)\) 560.2.bd.a 44 2
560.2.bd.b 52
560.2.be \(\chi_{560}(139, \cdot)\) 560.2.be.a 184 2
560.2.bi \(\chi_{560}(183, \cdot)\) None 0 2
560.2.bj \(\chi_{560}(97, \cdot)\) 560.2.bj.a 4 2
560.2.bj.b 8
560.2.bj.c 8
560.2.bj.d 24
560.2.bl \(\chi_{560}(267, \cdot)\) 560.2.bl.a 144 2
560.2.bn \(\chi_{560}(13, \cdot)\) 560.2.bn.a 184 2
560.2.bq \(\chi_{560}(199, \cdot)\) None 0 2
560.2.bs \(\chi_{560}(31, \cdot)\) 560.2.bs.a 8 2
560.2.bs.b 12
560.2.bs.c 12
560.2.bv \(\chi_{560}(9, \cdot)\) None 0 2
560.2.bw \(\chi_{560}(289, \cdot)\) 560.2.bw.a 4 2
560.2.bw.b 4
560.2.bw.c 4
560.2.bw.d 4
560.2.bw.e 4
560.2.bw.f 24
560.2.bz \(\chi_{560}(311, \cdot)\) None 0 2
560.2.cb \(\chi_{560}(121, \cdot)\) None 0 2
560.2.cc \(\chi_{560}(159, \cdot)\) 560.2.cc.a 4 2
560.2.cc.b 4
560.2.cc.c 4
560.2.cc.d 4
560.2.cc.e 8
560.2.cc.f 8
560.2.cc.g 8
560.2.cc.h 8
560.2.cf \(\chi_{560}(107, \cdot)\) 560.2.cf.a 368 4
560.2.ch \(\chi_{560}(117, \cdot)\) 560.2.ch.a 4 4
560.2.ch.b 4
560.2.ch.c 360
560.2.ci \(\chi_{560}(17, \cdot)\) 560.2.ci.a 4 4
560.2.ci.b 4
560.2.ci.c 16
560.2.ci.d 16
560.2.ci.e 48
560.2.cl \(\chi_{560}(23, \cdot)\) None 0 4
560.2.co \(\chi_{560}(19, \cdot)\) 560.2.co.a 368 4
560.2.cp \(\chi_{560}(221, \cdot)\) 560.2.cp.a 256 4
560.2.cq \(\chi_{560}(131, \cdot)\) 560.2.cq.a 256 4
560.2.cr \(\chi_{560}(109, \cdot)\) 560.2.cr.a 368 4
560.2.cu \(\chi_{560}(207, \cdot)\) 560.2.cu.a 8 4
560.2.cu.b 24
560.2.cu.c 32
560.2.cu.d 32
560.2.cx \(\chi_{560}(73, \cdot)\) None 0 4
560.2.cz \(\chi_{560}(157, \cdot)\) 560.2.cz.a 4 4
560.2.cz.b 4
560.2.cz.c 360
560.2.db \(\chi_{560}(67, \cdot)\) 560.2.db.a 368 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(560))\) into lower level spaces

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