# Properties

 Label 725.2 Level 725 Weight 2 Dimension 18757 Nonzero newspaces 24 Newform subspaces 83 Sturm bound 84000 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$725 = 5^{2} \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Newform subspaces: $$83$$ Sturm bound: $$84000$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(725))$$.

Total New Old
Modular forms 21784 19863 1921
Cusp forms 20217 18757 1460
Eisenstein series 1567 1106 461

## Trace form

 $$18757 q - 168 q^{2} - 170 q^{3} - 176 q^{4} - 214 q^{5} - 282 q^{6} - 178 q^{7} - 192 q^{8} - 188 q^{9} + O(q^{10})$$ $$18757 q - 168 q^{2} - 170 q^{3} - 176 q^{4} - 214 q^{5} - 282 q^{6} - 178 q^{7} - 192 q^{8} - 188 q^{9} - 234 q^{10} - 282 q^{11} - 218 q^{12} - 190 q^{13} - 210 q^{14} - 244 q^{15} - 288 q^{16} - 178 q^{17} - 190 q^{18} - 162 q^{19} - 204 q^{20} - 310 q^{21} - 182 q^{22} - 184 q^{23} - 226 q^{24} - 194 q^{25} - 597 q^{26} - 224 q^{27} - 224 q^{28} - 210 q^{29} - 468 q^{30} - 310 q^{31} - 274 q^{32} - 260 q^{33} - 255 q^{34} - 264 q^{35} - 412 q^{36} - 242 q^{37} - 250 q^{38} - 222 q^{39} - 254 q^{40} - 302 q^{41} - 154 q^{42} - 170 q^{43} - 204 q^{44} - 174 q^{45} - 352 q^{46} - 206 q^{47} - 222 q^{48} - 222 q^{49} - 174 q^{50} - 598 q^{51} - 250 q^{52} - 243 q^{53} - 268 q^{54} - 244 q^{55} - 440 q^{56} - 232 q^{57} - 360 q^{58} - 392 q^{59} - 204 q^{60} - 358 q^{61} - 232 q^{62} - 302 q^{63} - 322 q^{64} - 234 q^{65} - 442 q^{66} - 274 q^{67} - 272 q^{68} - 270 q^{69} - 284 q^{70} - 392 q^{71} - 366 q^{72} - 293 q^{73} - 268 q^{74} - 244 q^{75} - 686 q^{76} - 264 q^{77} - 350 q^{78} - 270 q^{79} - 234 q^{80} - 460 q^{81} - 230 q^{82} - 166 q^{83} - 420 q^{84} - 154 q^{85} - 436 q^{86} - 232 q^{87} - 472 q^{88} - 162 q^{89} - 174 q^{90} - 366 q^{91} - 386 q^{92} - 214 q^{93} - 186 q^{94} - 244 q^{95} - 560 q^{96} - 155 q^{97} - 366 q^{98} - 396 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(725))$$

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
725.2.a $$\chi_{725}(1, \cdot)$$ 725.2.a.a 1 1
725.2.a.b 2
725.2.a.c 2
725.2.a.d 3
725.2.a.e 3
725.2.a.f 4
725.2.a.g 4
725.2.a.h 5
725.2.a.i 5
725.2.a.j 5
725.2.a.k 5
725.2.a.l 6
725.2.b $$\chi_{725}(349, \cdot)$$ 725.2.b.a 2 1
725.2.b.b 4
725.2.b.c 4
725.2.b.d 6
725.2.b.e 6
725.2.b.f 10
725.2.b.g 10
725.2.c $$\chi_{725}(376, \cdot)$$ 725.2.c.a 2 1
725.2.c.b 2
725.2.c.c 2
725.2.c.d 4
725.2.c.e 6
725.2.c.f 8
725.2.c.g 10
725.2.c.h 10
725.2.d $$\chi_{725}(724, \cdot)$$ 725.2.d.a 4 1
725.2.d.b 8
725.2.d.c 12
725.2.d.d 20
725.2.e $$\chi_{725}(157, \cdot)$$ 725.2.e.a 4 2
725.2.e.b 16
725.2.e.c 26
725.2.e.d 40
725.2.j $$\chi_{725}(307, \cdot)$$ 725.2.j.a 4 2
725.2.j.b 16
725.2.j.c 26
725.2.j.d 40
725.2.k $$\chi_{725}(146, \cdot)$$ 725.2.k.a 4 4
725.2.k.b 128
725.2.k.c 148
725.2.l $$\chi_{725}(226, \cdot)$$ 725.2.l.a 6 6
725.2.l.b 6
725.2.l.c 6
725.2.l.d 24
725.2.l.e 36
725.2.l.f 54
725.2.l.g 54
725.2.l.h 84
725.2.m $$\chi_{725}(144, \cdot)$$ 725.2.m.a 288 4
725.2.n $$\chi_{725}(59, \cdot)$$ 725.2.n.a 128 4
725.2.n.b 152
725.2.o $$\chi_{725}(86, \cdot)$$ 725.2.o.a 296 4
725.2.p $$\chi_{725}(149, \cdot)$$ 725.2.p.a 24 6
725.2.p.b 48
725.2.p.c 72
725.2.p.d 120
725.2.q $$\chi_{725}(51, \cdot)$$ 725.2.q.a 12 6
725.2.q.b 24
725.2.q.c 36
725.2.q.d 60
725.2.q.e 60
725.2.q.f 72
725.2.r $$\chi_{725}(24, \cdot)$$ 725.2.r.a 12 6
725.2.r.b 12
725.2.r.c 48
725.2.r.d 72
725.2.r.e 108
725.2.s $$\chi_{725}(17, \cdot)$$ 725.2.s.a 584 8
725.2.x $$\chi_{725}(12, \cdot)$$ 725.2.x.a 584 8
725.2.y $$\chi_{725}(18, \cdot)$$ 725.2.y.a 120 12
725.2.y.b 156
725.2.y.c 240
725.2.bd $$\chi_{725}(43, \cdot)$$ 725.2.bd.a 120 12
725.2.bd.b 156
725.2.bd.c 240
725.2.be $$\chi_{725}(16, \cdot)$$ 725.2.be.a 1728 24
725.2.bf $$\chi_{725}(6, \cdot)$$ 725.2.bf.a 1776 24
725.2.bg $$\chi_{725}(54, \cdot)$$ 725.2.bg.a 1776 24
725.2.bh $$\chi_{725}(4, \cdot)$$ 725.2.bh.a 1728 24
725.2.bi $$\chi_{725}(3, \cdot)$$ 725.2.bi.a 3504 48
725.2.bn $$\chi_{725}(2, \cdot)$$ 725.2.bn.a 3504 48

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(725))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(725)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 2}$$