# Properties

 Label 775.2 Level 775 Weight 2 Dimension 21481 Nonzero newspaces 42 Newform subspaces 115 Sturm bound 96000 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$775 = 5^{2} \cdot 31$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$42$$ Newform subspaces: $$115$$ Sturm bound: $$96000$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(775))$$.

Total New Old
Modular forms 24840 22669 2171
Cusp forms 23161 21481 1680
Eisenstein series 1679 1188 491

## Trace form

 $$21481 q - 181 q^{2} - 183 q^{3} - 189 q^{4} - 230 q^{5} - 303 q^{6} - 191 q^{7} - 205 q^{8} - 201 q^{9} + O(q^{10})$$ $$21481 q - 181 q^{2} - 183 q^{3} - 189 q^{4} - 230 q^{5} - 303 q^{6} - 191 q^{7} - 205 q^{8} - 201 q^{9} - 250 q^{10} - 303 q^{11} - 231 q^{12} - 203 q^{13} - 223 q^{14} - 260 q^{15} - 309 q^{16} - 191 q^{17} - 203 q^{18} - 175 q^{19} - 220 q^{20} - 308 q^{21} - 197 q^{22} - 198 q^{23} - 215 q^{24} - 210 q^{25} - 633 q^{26} - 240 q^{27} - 247 q^{28} - 225 q^{29} - 260 q^{30} - 339 q^{31} - 516 q^{32} - 261 q^{33} - 293 q^{34} - 280 q^{35} - 429 q^{36} - 286 q^{37} - 265 q^{38} - 242 q^{39} - 270 q^{40} - 338 q^{41} - 197 q^{42} - 188 q^{43} - 203 q^{44} - 190 q^{45} - 303 q^{46} - 191 q^{47} - 168 q^{48} - 209 q^{49} - 190 q^{50} - 673 q^{51} - 226 q^{52} - 223 q^{53} - 320 q^{54} - 260 q^{55} - 470 q^{56} - 265 q^{57} - 320 q^{58} - 225 q^{59} - 220 q^{60} - 428 q^{61} - 261 q^{62} - 518 q^{63} - 329 q^{64} - 250 q^{65} - 576 q^{66} - 261 q^{67} - 292 q^{68} - 317 q^{69} - 300 q^{70} - 403 q^{71} - 390 q^{72} - 273 q^{73} - 258 q^{74} - 260 q^{75} - 740 q^{76} - 282 q^{77} - 386 q^{78} - 290 q^{79} - 250 q^{80} - 429 q^{81} - 247 q^{82} - 228 q^{83} - 403 q^{84} - 170 q^{85} - 423 q^{86} - 215 q^{87} - 315 q^{88} - 180 q^{89} - 190 q^{90} - 368 q^{91} - 426 q^{92} - 303 q^{93} - 398 q^{94} - 260 q^{95} - 568 q^{96} - 156 q^{97} - 377 q^{98} - 302 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(775))$$

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
775.2.a $$\chi_{775}(1, \cdot)$$ 775.2.a.a 1 1
775.2.a.b 1
775.2.a.c 1
775.2.a.d 2
775.2.a.e 4
775.2.a.f 4
775.2.a.g 4
775.2.a.h 5
775.2.a.i 5
775.2.a.j 5
775.2.a.k 5
775.2.a.l 10
775.2.b $$\chi_{775}(249, \cdot)$$ 775.2.b.a 2 1
775.2.b.b 2
775.2.b.c 2
775.2.b.d 4
775.2.b.e 8
775.2.b.f 8
775.2.b.g 10
775.2.b.h 10
775.2.e $$\chi_{775}(501, \cdot)$$ 775.2.e.a 2 2
775.2.e.b 2
775.2.e.c 4
775.2.e.d 4
775.2.e.e 4
775.2.e.f 8
775.2.e.g 8
775.2.e.h 18
775.2.e.i 18
775.2.e.j 28
775.2.f $$\chi_{775}(557, \cdot)$$ 775.2.f.a 4 2
775.2.f.b 4
775.2.f.c 8
775.2.f.d 8
775.2.f.e 12
775.2.f.f 16
775.2.f.g 40
775.2.h $$\chi_{775}(171, \cdot)$$ 775.2.h.a 312 4
775.2.i $$\chi_{775}(531, \cdot)$$ 775.2.i.a 312 4
775.2.j $$\chi_{775}(156, \cdot)$$ 775.2.j.a 4 4
775.2.j.b 140
775.2.j.c 160
775.2.k $$\chi_{775}(101, \cdot)$$ 775.2.k.a 4 4
775.2.k.b 4
775.2.k.c 4
775.2.k.d 24
775.2.k.e 24
775.2.k.f 36
775.2.k.g 36
775.2.k.h 56
775.2.l $$\chi_{775}(66, \cdot)$$ 775.2.l.a 312 4
775.2.m $$\chi_{775}(16, \cdot)$$ 775.2.m.a 312 4
775.2.o $$\chi_{775}(149, \cdot)$$ 775.2.o.a 4 2
775.2.o.b 4
775.2.o.c 8
775.2.o.d 8
775.2.o.e 16
775.2.o.f 16
775.2.o.g 36
775.2.r $$\chi_{775}(4, \cdot)$$ 775.2.r.a 312 4
775.2.x $$\chi_{775}(39, \cdot)$$ 775.2.x.a 312 4
775.2.bc $$\chi_{775}(94, \cdot)$$ 775.2.bc.a 136 4
775.2.bc.b 160
775.2.bd $$\chi_{775}(264, \cdot)$$ 775.2.bd.a 312 4
775.2.be $$\chi_{775}(219, \cdot)$$ 775.2.be.a 312 4
775.2.bf $$\chi_{775}(349, \cdot)$$ 775.2.bf.a 8 4
775.2.bf.b 8
775.2.bf.c 48
775.2.bf.d 48
775.2.bf.e 72
775.2.bj $$\chi_{775}(57, \cdot)$$ 775.2.bj.a 4 4
775.2.bj.b 4
775.2.bj.c 4
775.2.bj.d 4
775.2.bj.e 32
775.2.bj.f 48
775.2.bj.g 88
775.2.bk $$\chi_{775}(196, \cdot)$$ 775.2.bk.a 624 8
775.2.bl $$\chi_{775}(51, \cdot)$$ 775.2.bl.a 16 8
775.2.bl.b 40
775.2.bl.c 40
775.2.bl.d 88
775.2.bl.e 88
775.2.bl.f 112
775.2.bm $$\chi_{775}(36, \cdot)$$ 775.2.bm.a 8 8
775.2.bm.b 616
775.2.bn $$\chi_{775}(41, \cdot)$$ 775.2.bn.a 624 8
775.2.bo $$\chi_{775}(81, \cdot)$$ 775.2.bo.a 624 8
775.2.bp $$\chi_{775}(231, \cdot)$$ 775.2.bp.a 624 8
775.2.br $$\chi_{775}(263, \cdot)$$ 775.2.br.a 624 8
775.2.bs $$\chi_{775}(182, \cdot)$$ 775.2.bs.a 96 8
775.2.bs.b 112
775.2.bs.c 160
775.2.bx $$\chi_{775}(23, \cdot)$$ 775.2.bx.a 624 8
775.2.by $$\chi_{775}(27, \cdot)$$ 775.2.by.a 624 8
775.2.bz $$\chi_{775}(58, \cdot)$$ 775.2.bz.a 624 8
775.2.ca $$\chi_{775}(92, \cdot)$$ 775.2.ca.a 48 8
775.2.ca.b 576
775.2.cc $$\chi_{775}(59, \cdot)$$ 775.2.cc.a 624 8
775.2.ck $$\chi_{775}(49, \cdot)$$ 775.2.ck.a 32 8
775.2.ck.b 80
775.2.ck.c 80
775.2.ck.d 176
775.2.cl $$\chi_{775}(9, \cdot)$$ 775.2.cl.a 624 8
775.2.cm $$\chi_{775}(69, \cdot)$$ 775.2.cm.a 624 8
775.2.cn $$\chi_{775}(129, \cdot)$$ 775.2.cn.a 624 8
775.2.cs $$\chi_{775}(14, \cdot)$$ 775.2.cs.a 624 8
775.2.cu $$\chi_{775}(13, \cdot)$$ 775.2.cu.a 1248 16
775.2.cx $$\chi_{775}(37, \cdot)$$ 775.2.cx.a 1248 16
775.2.cy $$\chi_{775}(12, \cdot)$$ 775.2.cy.a 1248 16
775.2.cz $$\chi_{775}(3, \cdot)$$ 775.2.cz.a 1248 16
775.2.da $$\chi_{775}(48, \cdot)$$ 775.2.da.a 1248 16
775.2.df $$\chi_{775}(43, \cdot)$$ 775.2.df.a 160 16
775.2.df.b 224
775.2.df.c 352

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(775))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(775)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(155))$$$$^{\oplus 2}$$