# Properties

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

# Learn more

## Defining parameters

 Level: $$N$$ = $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Newform subspaces: $$104$$ 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

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

## 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

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