Properties

Label 561.2
Level 561
Weight 2
Dimension 8171
Nonzero newspaces 20
Newforms 46
Sturm bound 46080
Trace bound 4

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Defining parameters

Level: \( N \) = \( 561 = 3 \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newforms: \( 46 \)
Sturm bound: \(46080\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(561))\).

Total New Old
Modular forms 12160 8707 3453
Cusp forms 10881 8171 2710
Eisenstein series 1279 536 743

Trace form

\( 8171q + 9q^{2} - 51q^{3} - 87q^{4} + 18q^{5} - 55q^{6} - 104q^{7} + 5q^{8} - 71q^{9} + O(q^{10}) \) \( 8171q + 9q^{2} - 51q^{3} - 87q^{4} + 18q^{5} - 55q^{6} - 104q^{7} + 5q^{8} - 71q^{9} - 130q^{10} - 13q^{11} - 191q^{12} - 118q^{13} - 52q^{14} - 124q^{15} - 279q^{16} - 27q^{17} - 203q^{18} - 140q^{19} - 86q^{20} - 128q^{21} - 207q^{22} - 139q^{24} - 207q^{25} - 118q^{26} - 21q^{27} - 232q^{28} - 30q^{29} - 138q^{30} - 180q^{31} - 11q^{32} - 59q^{33} - 459q^{34} - 64q^{35} - 107q^{36} - 202q^{37} - 80q^{38} - 94q^{39} - 314q^{40} - 74q^{41} - 52q^{42} - 212q^{43} - 123q^{44} - 148q^{45} - 216q^{46} + 4q^{47} + q^{48} - 157q^{49} + 59q^{50} - 15q^{51} - 202q^{52} - 26q^{53} - 43q^{54} - 210q^{55} - 40q^{56} - 16q^{57} - 242q^{58} - 8q^{59} - 58q^{60} - 214q^{61} - 56q^{62} - 144q^{63} - 247q^{64} - 108q^{65} - 63q^{66} - 304q^{67} - 255q^{68} - 290q^{69} - 520q^{70} - 96q^{71} - 191q^{72} - 466q^{73} - 174q^{74} - 307q^{75} - 548q^{76} - 156q^{77} - 434q^{78} - 384q^{79} - 406q^{80} - 183q^{81} - 382q^{82} - 232q^{83} - 224q^{84} - 278q^{85} - 12q^{86} - 94q^{87} - 291q^{88} + 14q^{89} + 14q^{90} - 184q^{91} - 156q^{92} - 54q^{93} - 232q^{94} - 68q^{95} + 85q^{96} - 182q^{97} - 71q^{98} - 59q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(561))\)

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
561.2.a \(\chi_{561}(1, \cdot)\) 561.2.a.a 1 1
561.2.a.b 1
561.2.a.c 1
561.2.a.d 1
561.2.a.e 2
561.2.a.f 2
561.2.a.g 3
561.2.a.h 3
561.2.a.i 3
561.2.a.j 4
561.2.a.k 6
561.2.f \(\chi_{561}(494, \cdot)\) 561.2.f.a 32 1
561.2.f.b 32
561.2.g \(\chi_{561}(67, \cdot)\) 561.2.g.a 12 1
561.2.g.b 16
561.2.h \(\chi_{561}(560, \cdot)\) 561.2.h.a 4 1
561.2.h.b 4
561.2.h.c 4
561.2.h.d 56
561.2.i \(\chi_{561}(98, \cdot)\) 561.2.i.a 136 2
561.2.j \(\chi_{561}(166, \cdot)\) 561.2.j.a 4 2
561.2.j.b 4
561.2.j.c 20
561.2.j.d 28
561.2.m \(\chi_{561}(103, \cdot)\) 561.2.m.a 4 4
561.2.m.b 4
561.2.m.c 16
561.2.m.d 24
561.2.m.e 40
561.2.m.f 40
561.2.o \(\chi_{561}(100, \cdot)\) 561.2.o.a 56 4
561.2.o.b 72
561.2.q \(\chi_{561}(32, \cdot)\) 561.2.q.a 272 4
561.2.r \(\chi_{561}(50, \cdot)\) 561.2.r.a 16 4
561.2.r.b 256
561.2.s \(\chi_{561}(16, \cdot)\) 561.2.s.a 144 4
561.2.t \(\chi_{561}(35, \cdot)\) 561.2.t.a 128 4
561.2.t.b 128
561.2.y \(\chi_{561}(10, \cdot)\) 561.2.y.a 288 8
561.2.z \(\chi_{561}(23, \cdot)\) 561.2.z.a 480 8
561.2.be \(\chi_{561}(4, \cdot)\) 561.2.be.a 288 8
561.2.bf \(\chi_{561}(140, \cdot)\) 561.2.bf.a 544 8
561.2.bg \(\chi_{561}(2, \cdot)\) 561.2.bg.a 1088 16
561.2.bi \(\chi_{561}(25, \cdot)\) 561.2.bi.a 576 16
561.2.bm \(\chi_{561}(5, \cdot)\) 561.2.bm.a 2176 32
561.2.bn \(\chi_{561}(7, \cdot)\) 561.2.bn.a 1152 32

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(561))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(561)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 2}\)