Properties

Label 525.2
Level 525
Weight 2
Dimension 6152
Nonzero newspaces 24
Newforms 104
Sturm bound 38400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newforms: \( 104 \)
Sturm bound: \(38400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(525))\).

Total New Old
Modular forms 10272 6564 3708
Cusp forms 8929 6152 2777
Eisenstein series 1343 412 931

Trace form

\( 6152q + 2q^{2} - 20q^{3} - 20q^{4} + 12q^{5} - 8q^{6} - 42q^{7} + 60q^{8} - 6q^{9} + O(q^{10}) \) \( 6152q + 2q^{2} - 20q^{3} - 20q^{4} + 12q^{5} - 8q^{6} - 42q^{7} + 60q^{8} - 6q^{9} - 28q^{10} + 26q^{11} + 12q^{12} + 2q^{13} + 48q^{14} - 68q^{15} - 24q^{16} + 16q^{17} - 34q^{18} - 42q^{19} - 72q^{20} - 50q^{21} - 152q^{22} - 8q^{23} - 216q^{24} - 148q^{25} - 42q^{26} - 86q^{27} - 242q^{28} - 88q^{29} - 148q^{30} - 122q^{31} - 256q^{32} - 118q^{33} - 212q^{34} - 52q^{35} - 332q^{36} - 120q^{37} - 154q^{38} - 166q^{39} - 244q^{40} - 28q^{41} - 234q^{42} - 216q^{43} - 204q^{44} - 212q^{45} - 168q^{46} - 26q^{47} - 292q^{48} - 22q^{49} - 212q^{50} - 144q^{51} - 368q^{52} - 64q^{53} - 266q^{54} - 152q^{55} - 90q^{56} - 240q^{57} - 424q^{58} - 164q^{59} - 196q^{60} - 238q^{61} - 308q^{62} - 34q^{63} - 384q^{64} - 28q^{65} - 196q^{66} - 166q^{67} - 152q^{68} - 20q^{69} - 316q^{70} - 20q^{71} + 132q^{72} - 184q^{73} - 158q^{74} + 84q^{75} - 428q^{76} - 120q^{77} - 76q^{78} - 178q^{79} + 92q^{80} + 54q^{81} - 316q^{82} - 52q^{83} + 68q^{84} - 364q^{85} - 58q^{86} + 40q^{87} - 392q^{88} - 84q^{89} + 96q^{90} - 28q^{91} + 104q^{92} + 4q^{93} - 260q^{94} - 112q^{95} + 276q^{96} - 284q^{97} + 48q^{98} + 140q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)

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
525.2.a \(\chi_{525}(1, \cdot)\) 525.2.a.a 1 1
525.2.a.b 1
525.2.a.c 1
525.2.a.d 1
525.2.a.e 2
525.2.a.f 2
525.2.a.g 2
525.2.a.h 2
525.2.a.i 2
525.2.a.j 3
525.2.a.k 3
525.2.b \(\chi_{525}(251, \cdot)\) 525.2.b.a 2 1
525.2.b.b 2
525.2.b.c 2
525.2.b.d 2
525.2.b.e 4
525.2.b.f 4
525.2.b.g 4
525.2.b.h 8
525.2.b.i 8
525.2.b.j 8
525.2.d \(\chi_{525}(274, \cdot)\) 525.2.d.a 2 1
525.2.d.b 2
525.2.d.c 4
525.2.d.d 4
525.2.d.e 4
525.2.g \(\chi_{525}(524, \cdot)\) 525.2.g.a 4 1
525.2.g.b 4
525.2.g.c 4
525.2.g.d 8
525.2.g.e 8
525.2.g.f 16
525.2.i \(\chi_{525}(151, \cdot)\) 525.2.i.a 2 2
525.2.i.b 2
525.2.i.c 2
525.2.i.d 2
525.2.i.e 2
525.2.i.f 4
525.2.i.g 4
525.2.i.h 8
525.2.i.i 8
525.2.i.j 8
525.2.i.k 8
525.2.j \(\chi_{525}(218, \cdot)\) 525.2.j.a 16 2
525.2.j.b 24
525.2.j.c 32
525.2.m \(\chi_{525}(118, \cdot)\) 525.2.m.a 8 2
525.2.m.b 16
525.2.m.c 24
525.2.n \(\chi_{525}(106, \cdot)\) 525.2.n.a 4 4
525.2.n.b 20
525.2.n.c 24
525.2.n.d 32
525.2.n.e 32
525.2.q \(\chi_{525}(299, \cdot)\) 525.2.q.a 4 2
525.2.q.b 4
525.2.q.c 4
525.2.q.d 4
525.2.q.e 16
525.2.q.f 16
525.2.q.g 40
525.2.r \(\chi_{525}(424, \cdot)\) 525.2.r.a 4 2
525.2.r.b 4
525.2.r.c 4
525.2.r.d 4
525.2.r.e 4
525.2.r.f 4
525.2.r.g 8
525.2.r.h 16
525.2.t \(\chi_{525}(26, \cdot)\) 525.2.t.a 2 2
525.2.t.b 2
525.2.t.c 2
525.2.t.d 2
525.2.t.e 2
525.2.t.f 8
525.2.t.g 8
525.2.t.h 20
525.2.t.i 20
525.2.t.j 24
525.2.w \(\chi_{525}(104, \cdot)\) 525.2.w.a 304 4
525.2.z \(\chi_{525}(64, \cdot)\) 525.2.z.a 56 4
525.2.z.b 72
525.2.bb \(\chi_{525}(41, \cdot)\) 525.2.bb.a 304 4
525.2.bc \(\chi_{525}(82, \cdot)\) 525.2.bc.a 8 4
525.2.bc.b 8
525.2.bc.c 24
525.2.bc.d 24
525.2.bc.e 32
525.2.bf \(\chi_{525}(32, \cdot)\) 525.2.bf.a 8 4
525.2.bf.b 8
525.2.bf.c 8
525.2.bf.d 8
525.2.bf.e 16
525.2.bf.f 48
525.2.bf.g 80
525.2.bg \(\chi_{525}(16, \cdot)\) 525.2.bg.a 160 8
525.2.bg.b 160
525.2.bh \(\chi_{525}(13, \cdot)\) 525.2.bh.a 320 8
525.2.bk \(\chi_{525}(8, \cdot)\) 525.2.bk.a 480 8
525.2.bm \(\chi_{525}(131, \cdot)\) 525.2.bm.a 608 8
525.2.bo \(\chi_{525}(4, \cdot)\) 525.2.bo.a 320 8
525.2.bp \(\chi_{525}(59, \cdot)\) 525.2.bp.a 608 8
525.2.bs \(\chi_{525}(2, \cdot)\) 525.2.bs.a 1216 16
525.2.bv \(\chi_{525}(52, \cdot)\) 525.2.bv.a 640 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(525))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(525)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)