Properties

Label 532.2
Level 532
Weight 2
Dimension 4634
Nonzero newspaces 32
Newform subspaces 57
Sturm bound 34560
Trace bound 10

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Defining parameters

Level: \( N \) = \( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Newform subspaces: \( 57 \)
Sturm bound: \(34560\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(532))\).

Total New Old
Modular forms 9180 4970 4210
Cusp forms 8101 4634 3467
Eisenstein series 1079 336 743

Trace form

\( 4634 q - 30 q^{2} + 2 q^{3} - 30 q^{4} - 54 q^{5} - 36 q^{6} + 8 q^{7} - 84 q^{8} - 64 q^{9} + O(q^{10}) \) \( 4634 q - 30 q^{2} + 2 q^{3} - 30 q^{4} - 54 q^{5} - 36 q^{6} + 8 q^{7} - 84 q^{8} - 64 q^{9} - 48 q^{10} - 6 q^{11} - 60 q^{12} - 56 q^{13} - 63 q^{14} + 24 q^{15} - 54 q^{16} - 36 q^{17} - 60 q^{18} + 41 q^{19} - 72 q^{20} - 79 q^{21} - 54 q^{22} + 24 q^{23} - 12 q^{24} - 40 q^{25} - 12 q^{26} + 26 q^{27} - 18 q^{28} - 216 q^{29} - 150 q^{30} - 50 q^{31} - 120 q^{32} - 198 q^{33} - 126 q^{34} - 66 q^{35} - 288 q^{36} - 158 q^{37} - 180 q^{38} - 104 q^{39} - 186 q^{40} - 132 q^{41} - 159 q^{42} - 50 q^{43} - 162 q^{44} - 138 q^{45} - 150 q^{46} - 162 q^{48} - 76 q^{49} - 150 q^{50} + 78 q^{51} - 36 q^{52} + 42 q^{53} + 54 q^{54} + 108 q^{55} - 72 q^{56} - 52 q^{57} - 60 q^{58} + 108 q^{59} - 30 q^{60} - 50 q^{61} + 54 q^{62} + 32 q^{63} + 36 q^{64} - 102 q^{65} + 120 q^{66} - 44 q^{67} + 90 q^{68} - 318 q^{69} + 51 q^{70} + 18 q^{71} + 264 q^{72} - 290 q^{73} + 96 q^{74} - 76 q^{75} + 144 q^{76} - 339 q^{77} + 6 q^{78} - 74 q^{79} + 156 q^{80} - 232 q^{81} + 210 q^{82} - 30 q^{83} + 63 q^{84} - 456 q^{85} + 126 q^{86} + 60 q^{87} + 72 q^{88} - 204 q^{89} + 18 q^{90} + 28 q^{91} + 12 q^{92} - 38 q^{93} + 6 q^{94} - 21 q^{95} - 168 q^{96} - 50 q^{97} - 114 q^{98} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(532))\)

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
532.2.a \(\chi_{532}(1, \cdot)\) 532.2.a.a 1 1
532.2.a.b 2
532.2.a.c 2
532.2.a.d 2
532.2.a.e 3
532.2.f \(\chi_{532}(419, \cdot)\) 532.2.f.a 4 1
532.2.f.b 4
532.2.f.c 32
532.2.f.d 32
532.2.g \(\chi_{532}(265, \cdot)\) 532.2.g.a 4 1
532.2.g.b 8
532.2.h \(\chi_{532}(379, \cdot)\) 532.2.h.a 4 1
532.2.h.b 4
532.2.h.c 52
532.2.i \(\chi_{532}(305, \cdot)\) 532.2.i.a 4 2
532.2.i.b 6
532.2.i.c 14
532.2.j \(\chi_{532}(197, \cdot)\) 532.2.j.a 2 2
532.2.j.b 8
532.2.j.c 10
532.2.k \(\chi_{532}(121, \cdot)\) 532.2.k.a 4 2
532.2.k.b 24
532.2.l \(\chi_{532}(429, \cdot)\) 532.2.l.a 4 2
532.2.l.b 24
532.2.q \(\chi_{532}(145, \cdot)\) 532.2.q.a 28 2
532.2.r \(\chi_{532}(87, \cdot)\) 532.2.r.a 4 2
532.2.r.b 148
532.2.s \(\chi_{532}(183, \cdot)\) 532.2.s.a 120 2
532.2.t \(\chi_{532}(151, \cdot)\) 532.2.t.a 152 2
532.2.u \(\chi_{532}(83, \cdot)\) 532.2.u.a 16 2
532.2.u.b 136
532.2.v \(\chi_{532}(341, \cdot)\) 532.2.v.a 2 2
532.2.v.b 2
532.2.v.c 4
532.2.v.d 4
532.2.v.e 16
532.2.w \(\chi_{532}(115, \cdot)\) 532.2.w.a 72 2
532.2.w.b 72
532.2.x \(\chi_{532}(69, \cdot)\) 532.2.x.a 24 2
532.2.y \(\chi_{532}(107, \cdot)\) 532.2.y.a 152 2
532.2.bl \(\chi_{532}(331, \cdot)\) 532.2.bl.a 152 2
532.2.bm \(\chi_{532}(297, \cdot)\) 532.2.bm.a 28 2
532.2.bn \(\chi_{532}(311, \cdot)\) 532.2.bn.a 4 2
532.2.bn.b 148
532.2.bo \(\chi_{532}(85, \cdot)\) 532.2.bo.a 30 6
532.2.bo.b 30
532.2.bp \(\chi_{532}(9, \cdot)\) 532.2.bp.a 78 6
532.2.bq \(\chi_{532}(25, \cdot)\) 532.2.bq.a 78 6
532.2.br \(\chi_{532}(131, \cdot)\) 532.2.br.a 456 6
532.2.bs \(\chi_{532}(67, \cdot)\) 532.2.bs.a 456 6
532.2.bv \(\chi_{532}(13, \cdot)\) 532.2.bv.a 84 6
532.2.bw \(\chi_{532}(89, \cdot)\) 532.2.bw.a 78 6
532.2.cb \(\chi_{532}(15, \cdot)\) 532.2.cb.a 360 6
532.2.cc \(\chi_{532}(55, \cdot)\) 532.2.cc.a 456 6
532.2.cd \(\chi_{532}(47, \cdot)\) 532.2.cd.a 456 6
532.2.ce \(\chi_{532}(51, \cdot)\) 532.2.ce.a 456 6
532.2.cj \(\chi_{532}(33, \cdot)\) 532.2.cj.a 78 6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(532))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(532)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(532))\)\(^{\oplus 1}\)