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

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

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

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