# Properties

 Label 637.2 Level 637 Weight 2 Dimension 15079 Nonzero newspaces 30 Newform subspaces 142 Sturm bound 65856 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$30$$ Newform subspaces: $$142$$ Sturm bound: $$65856$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(637))$$.

Total New Old
Modular forms 17184 16145 1039
Cusp forms 15745 15079 666
Eisenstein series 1439 1066 373

## Trace form

 $$15079 q - 150 q^{2} - 152 q^{3} - 158 q^{4} - 156 q^{5} - 168 q^{6} - 188 q^{7} - 291 q^{8} - 178 q^{9} + O(q^{10})$$ $$15079 q - 150 q^{2} - 152 q^{3} - 158 q^{4} - 156 q^{5} - 168 q^{6} - 188 q^{7} - 291 q^{8} - 178 q^{9} - 195 q^{10} - 174 q^{11} - 226 q^{12} - 191 q^{13} - 432 q^{14} - 312 q^{15} - 226 q^{16} - 189 q^{17} - 255 q^{18} - 204 q^{19} - 261 q^{20} - 230 q^{21} - 354 q^{22} - 204 q^{23} - 324 q^{24} - 227 q^{25} - 237 q^{26} - 446 q^{27} - 272 q^{28} - 339 q^{29} - 360 q^{30} - 234 q^{31} - 336 q^{32} - 282 q^{33} - 300 q^{34} - 258 q^{35} - 410 q^{36} - 181 q^{37} - 222 q^{38} - 204 q^{39} - 330 q^{40} - 189 q^{41} - 174 q^{42} - 302 q^{43} - 138 q^{44} - 165 q^{45} - 120 q^{46} - 198 q^{47} - 150 q^{48} - 104 q^{49} - 573 q^{50} - 198 q^{51} - 192 q^{52} - 402 q^{53} - 234 q^{54} - 144 q^{55} - 132 q^{56} - 402 q^{57} - 231 q^{58} - 222 q^{59} - 390 q^{60} - 227 q^{61} - 336 q^{62} - 300 q^{63} - 485 q^{64} - 330 q^{65} - 750 q^{66} - 336 q^{67} - 519 q^{68} - 414 q^{69} - 426 q^{70} - 456 q^{71} - 288 q^{72} - 336 q^{73} - 351 q^{74} - 346 q^{75} - 180 q^{76} - 234 q^{77} - 237 q^{78} - 262 q^{79} - 9 q^{80} - 10 q^{81} + 279 q^{82} - 6 q^{83} + 232 q^{84} + 39 q^{85} + 48 q^{86} + 264 q^{87} + 648 q^{88} + 36 q^{89} + 756 q^{90} - 53 q^{91} - 192 q^{92} + 282 q^{93} + 522 q^{94} + 132 q^{95} + 768 q^{96} + 222 q^{97} + 264 q^{98} - 156 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(637))$$

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
637.2.a $$\chi_{637}(1, \cdot)$$ 637.2.a.a 1 1
637.2.a.b 1
637.2.a.c 1
637.2.a.d 1
637.2.a.e 2
637.2.a.f 2
637.2.a.g 2
637.2.a.h 3
637.2.a.i 3
637.2.a.j 3
637.2.a.k 5
637.2.a.l 5
637.2.a.m 6
637.2.a.n 6
637.2.c $$\chi_{637}(246, \cdot)$$ 637.2.c.a 2 1
637.2.c.b 2
637.2.c.c 2
637.2.c.d 6
637.2.c.e 8
637.2.c.f 8
637.2.c.g 16
637.2.e $$\chi_{637}(79, \cdot)$$ 637.2.e.a 2 2
637.2.e.b 2
637.2.e.c 2
637.2.e.d 2
637.2.e.e 2
637.2.e.f 4
637.2.e.g 4
637.2.e.h 4
637.2.e.i 6
637.2.e.j 6
637.2.e.k 6
637.2.e.l 6
637.2.e.m 10
637.2.e.n 12
637.2.e.o 12
637.2.f $$\chi_{637}(295, \cdot)$$ 637.2.f.a 2 2
637.2.f.b 2
637.2.f.c 4
637.2.f.d 4
637.2.f.e 4
637.2.f.f 4
637.2.f.g 8
637.2.f.h 8
637.2.f.i 8
637.2.f.j 12
637.2.f.k 12
637.2.f.l 16
637.2.g $$\chi_{637}(263, \cdot)$$ 637.2.g.a 2 2
637.2.g.b 4
637.2.g.c 4
637.2.g.d 4
637.2.g.e 4
637.2.g.f 4
637.2.g.g 4
637.2.g.h 8
637.2.g.i 8
637.2.g.j 8
637.2.g.k 8
637.2.g.l 12
637.2.g.m 16
637.2.h $$\chi_{637}(165, \cdot)$$ 637.2.h.a 2 2
637.2.h.b 4
637.2.h.c 4
637.2.h.d 4
637.2.h.e 4
637.2.h.f 4
637.2.h.g 4
637.2.h.h 8
637.2.h.i 8
637.2.h.j 8
637.2.h.k 8
637.2.h.l 12
637.2.h.m 16
637.2.i $$\chi_{637}(489, \cdot)$$ 637.2.i.a 32 2
637.2.i.b 56
637.2.k $$\chi_{637}(459, \cdot)$$ 637.2.k.a 2 2
637.2.k.b 2
637.2.k.c 2
637.2.k.d 4
637.2.k.e 4
637.2.k.f 4
637.2.k.g 12
637.2.k.h 12
637.2.k.i 12
637.2.k.j 32
637.2.q $$\chi_{637}(491, \cdot)$$ 637.2.q.a 2 2
637.2.q.b 2
637.2.q.c 2
637.2.q.d 4
637.2.q.e 4
637.2.q.f 4
637.2.q.g 12
637.2.q.h 12
637.2.q.i 12
637.2.q.j 32
637.2.r $$\chi_{637}(116, \cdot)$$ 637.2.r.a 4 2
637.2.r.b 4
637.2.r.c 4
637.2.r.d 12
637.2.r.e 12
637.2.r.f 16
637.2.r.g 32
637.2.u $$\chi_{637}(30, \cdot)$$ 637.2.u.a 2 2
637.2.u.b 2
637.2.u.c 2
637.2.u.d 4
637.2.u.e 4
637.2.u.f 4
637.2.u.g 12
637.2.u.h 12
637.2.u.i 12
637.2.u.j 32
637.2.w $$\chi_{637}(92, \cdot)$$ 637.2.w.a 162 6
637.2.w.b 174
637.2.x $$\chi_{637}(19, \cdot)$$ 637.2.x.a 28 4
637.2.x.b 32
637.2.x.c 112
637.2.bb $$\chi_{637}(227, \cdot)$$ 637.2.bb.a 28 4
637.2.bb.b 32
637.2.bb.c 112
637.2.bc $$\chi_{637}(31, \cdot)$$ 637.2.bc.a 24 4
637.2.bc.b 32
637.2.bc.c 112
637.2.bd $$\chi_{637}(97, \cdot)$$ 637.2.bd.a 28 4
637.2.bd.b 28
637.2.bd.c 112
637.2.bg $$\chi_{637}(64, \cdot)$$ 637.2.bg.a 372 6
637.2.bi $$\chi_{637}(16, \cdot)$$ 637.2.bi.a 756 12
637.2.bj $$\chi_{637}(9, \cdot)$$ 637.2.bj.a 756 12
637.2.bk $$\chi_{637}(22, \cdot)$$ 637.2.bk.a 768 12
637.2.bl $$\chi_{637}(53, \cdot)$$ 637.2.bl.a 324 12
637.2.bl.b 348
637.2.bn $$\chi_{637}(34, \cdot)$$ 637.2.bn.a 744 12
637.2.bp $$\chi_{637}(88, \cdot)$$ 637.2.bp.a 756 12
637.2.bs $$\chi_{637}(25, \cdot)$$ 637.2.bs.a 768 12
637.2.bt $$\chi_{637}(36, \cdot)$$ 637.2.bt.a 768 12
637.2.bz $$\chi_{637}(4, \cdot)$$ 637.2.bz.a 756 12
637.2.cb $$\chi_{637}(6, \cdot)$$ 637.2.cb.a 1536 24
637.2.cc $$\chi_{637}(5, \cdot)$$ 637.2.cc.a 1536 24
637.2.cd $$\chi_{637}(45, \cdot)$$ 637.2.cd.a 1512 24
637.2.ch $$\chi_{637}(24, \cdot)$$ 637.2.ch.a 1512 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(637))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(637)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(637))$$$$^{\oplus 1}$$