# Properties

 Label 625.2 Level 625 Weight 2 Dimension 14016 Nonzero newspaces 8 Newform subspaces 45 Sturm bound 62500 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$625 = 5^{4}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$45$$ Sturm bound: $$62500$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(625))$$.

Total New Old
Modular forms 16175 14784 1391
Cusp forms 15076 14016 1060
Eisenstein series 1099 768 331

## Trace form

 $$14016 q - 160 q^{2} - 160 q^{3} - 160 q^{4} - 200 q^{5} - 288 q^{6} - 160 q^{7} - 160 q^{8} - 160 q^{9} + O(q^{10})$$ $$14016 q - 160 q^{2} - 160 q^{3} - 160 q^{4} - 200 q^{5} - 288 q^{6} - 160 q^{7} - 160 q^{8} - 160 q^{9} - 200 q^{10} - 288 q^{11} - 160 q^{12} - 160 q^{13} - 160 q^{14} - 200 q^{15} - 304 q^{16} - 170 q^{17} - 185 q^{18} - 180 q^{19} - 200 q^{20} - 308 q^{21} - 200 q^{22} - 180 q^{23} - 230 q^{24} - 200 q^{25} - 438 q^{26} - 190 q^{27} - 220 q^{28} - 180 q^{29} - 200 q^{30} - 308 q^{31} - 195 q^{32} - 180 q^{33} - 185 q^{34} - 200 q^{35} - 344 q^{36} - 165 q^{37} - 190 q^{38} - 200 q^{39} - 200 q^{40} - 308 q^{41} - 260 q^{42} - 200 q^{43} - 230 q^{44} - 200 q^{45} - 348 q^{46} - 200 q^{47} - 310 q^{48} - 215 q^{49} - 200 q^{50} - 478 q^{51} - 270 q^{52} - 205 q^{53} - 290 q^{54} - 200 q^{55} - 380 q^{56} - 240 q^{57} - 230 q^{58} - 210 q^{59} - 200 q^{60} - 328 q^{61} - 270 q^{62} - 250 q^{63} - 270 q^{64} - 200 q^{65} - 396 q^{66} - 200 q^{67} - 280 q^{68} - 230 q^{69} - 200 q^{70} - 328 q^{71} - 330 q^{72} - 200 q^{73} - 270 q^{74} - 200 q^{75} - 530 q^{76} - 240 q^{77} - 290 q^{78} - 200 q^{79} - 200 q^{80} - 364 q^{81} - 280 q^{82} - 270 q^{83} - 360 q^{84} - 200 q^{85} - 408 q^{86} - 290 q^{87} - 360 q^{88} - 285 q^{89} - 200 q^{90} - 388 q^{91} - 300 q^{92} - 290 q^{93} - 320 q^{94} - 200 q^{95} - 188 q^{96} - 300 q^{97} - 320 q^{98} - 290 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(625))$$

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
625.2.a $$\chi_{625}(1, \cdot)$$ 625.2.a.a 2 1
625.2.a.b 2
625.2.a.c 2
625.2.a.d 2
625.2.a.e 8
625.2.a.f 8
625.2.a.g 8
625.2.b $$\chi_{625}(624, \cdot)$$ 625.2.b.a 4 1
625.2.b.b 4
625.2.b.c 8
625.2.b.d 16
625.2.d $$\chi_{625}(126, \cdot)$$ 625.2.d.a 4 4
625.2.d.b 4
625.2.d.c 4
625.2.d.d 4
625.2.d.e 4
625.2.d.f 4
625.2.d.g 4
625.2.d.h 4
625.2.d.i 4
625.2.d.j 4
625.2.d.k 8
625.2.d.l 8
625.2.d.m 16
625.2.d.n 16
625.2.d.o 16
625.2.d.p 16
625.2.d.q 16
625.2.e $$\chi_{625}(124, \cdot)$$ 625.2.e.a 8 4
625.2.e.b 8
625.2.e.c 8
625.2.e.d 8
625.2.e.e 8
625.2.e.f 8
625.2.e.g 8
625.2.e.h 8
625.2.e.i 8
625.2.e.j 32
625.2.e.k 32
625.2.g $$\chi_{625}(26, \cdot)$$ 625.2.g.a 220 20
625.2.g.b 480
625.2.h $$\chi_{625}(24, \cdot)$$ 625.2.h.a 240 20
625.2.h.b 440
625.2.j $$\chi_{625}(6, \cdot)$$ 625.2.j.a 6100 100
625.2.k $$\chi_{625}(4, \cdot)$$ 625.2.k.a 6200 100

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(625))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(625)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(125))$$$$^{\oplus 2}$$