# Properties

 Label 931.2 Level 931 Weight 2 Dimension 32844 Nonzero newspaces 32 Newform subspaces 154 Sturm bound 141120 Trace bound 10

## Defining parameters

 Level: $$N$$ = $$931 = 7^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Newform subspaces: $$154$$ Sturm bound: $$141120$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(931))$$.

Total New Old
Modular forms 36360 34492 1868
Cusp forms 34201 32844 1357
Eisenstein series 2159 1648 511

## Trace form

 $$32844 q - 243 q^{2} - 245 q^{3} - 251 q^{4} - 249 q^{5} - 261 q^{6} - 296 q^{7} - 447 q^{8} - 263 q^{9} + O(q^{10})$$ $$32844 q - 243 q^{2} - 245 q^{3} - 251 q^{4} - 249 q^{5} - 261 q^{6} - 296 q^{7} - 447 q^{8} - 263 q^{9} - 273 q^{10} - 261 q^{11} - 305 q^{12} - 277 q^{13} - 324 q^{14} - 483 q^{15} - 335 q^{16} - 282 q^{17} - 351 q^{18} - 299 q^{19} - 636 q^{20} - 338 q^{21} - 516 q^{22} - 294 q^{23} - 393 q^{24} - 317 q^{25} - 339 q^{26} - 338 q^{27} - 380 q^{28} - 495 q^{29} - 444 q^{30} - 319 q^{31} - 408 q^{32} - 387 q^{33} - 390 q^{34} - 366 q^{35} - 599 q^{36} - 284 q^{37} - 339 q^{38} - 584 q^{39} - 246 q^{40} - 255 q^{41} - 282 q^{42} - 460 q^{43} - 225 q^{44} - 264 q^{45} - 210 q^{46} - 294 q^{47} - 261 q^{48} - 212 q^{49} - 870 q^{50} - 267 q^{51} - 191 q^{52} - 297 q^{53} - 306 q^{54} - 207 q^{55} - 240 q^{56} - 539 q^{57} - 564 q^{58} - 318 q^{59} - 474 q^{60} - 329 q^{61} - 444 q^{62} - 408 q^{63} - 665 q^{64} - 504 q^{65} - 669 q^{66} - 466 q^{67} - 615 q^{68} - 528 q^{69} - 534 q^{70} - 624 q^{71} - 825 q^{72} - 469 q^{73} - 555 q^{74} - 578 q^{75} - 488 q^{76} - 774 q^{77} - 681 q^{78} - 499 q^{79} - 645 q^{80} - 428 q^{81} - 450 q^{82} - 300 q^{83} - 212 q^{84} - 573 q^{85} - 306 q^{86} - 285 q^{87} - 297 q^{88} - 330 q^{89} - 114 q^{90} - 310 q^{91} - 576 q^{92} - 91 q^{93} - 264 q^{94} - 273 q^{95} - 438 q^{96} - 286 q^{97} + 12 q^{98} - 864 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(931))$$

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
931.2.a $$\chi_{931}(1, \cdot)$$ 931.2.a.a 1 1
931.2.a.b 1
931.2.a.c 1
931.2.a.d 2
931.2.a.e 2
931.2.a.f 2
931.2.a.g 2
931.2.a.h 2
931.2.a.i 2
931.2.a.j 2
931.2.a.k 3
931.2.a.l 4
931.2.a.m 4
931.2.a.n 7
931.2.a.o 7
931.2.a.p 10
931.2.a.q 10
931.2.c $$\chi_{931}(930, \cdot)$$ 931.2.c.a 4 1
931.2.c.b 4
931.2.c.c 4
931.2.c.d 6
931.2.c.e 6
931.2.c.f 40
931.2.e $$\chi_{931}(197, \cdot)$$ 931.2.e.a 4 2
931.2.e.b 6
931.2.e.c 10
931.2.e.d 20
931.2.e.e 24
931.2.e.f 24
931.2.e.g 40
931.2.f $$\chi_{931}(324, \cdot)$$ 931.2.f.a 2 2
931.2.f.b 2
931.2.f.c 2
931.2.f.d 4
931.2.f.e 4
931.2.f.f 4
931.2.f.g 4
931.2.f.h 4
931.2.f.i 4
931.2.f.j 4
931.2.f.k 4
931.2.f.l 6
931.2.f.m 6
931.2.f.n 8
931.2.f.o 8
931.2.f.p 14
931.2.f.q 20
931.2.f.r 20
931.2.g $$\chi_{931}(30, \cdot)$$ 931.2.g.a 4 2
931.2.g.b 4
931.2.g.c 6
931.2.g.d 6
931.2.g.e 10
931.2.g.f 10
931.2.g.g 20
931.2.g.h 24
931.2.g.i 40
931.2.h $$\chi_{931}(410, \cdot)$$ 931.2.h.a 4 2
931.2.h.b 4
931.2.h.c 6
931.2.h.d 6
931.2.h.e 10
931.2.h.f 10
931.2.h.g 20
931.2.h.h 24
931.2.h.i 40
931.2.i $$\chi_{931}(411, \cdot)$$ 931.2.i.a 2 2
931.2.i.b 2
931.2.i.c 4
931.2.i.d 4
931.2.i.e 4
931.2.i.f 12
931.2.i.g 16
931.2.i.h 80
931.2.o $$\chi_{931}(227, \cdot)$$ 931.2.o.a 4 2
931.2.o.b 4
931.2.o.c 4
931.2.o.d 4
931.2.o.e 6
931.2.o.f 6
931.2.o.g 8
931.2.o.h 8
931.2.o.i 80
931.2.p $$\chi_{931}(293, \cdot)$$ 931.2.p.a 2 2
931.2.p.b 2
931.2.p.c 2
931.2.p.d 2
931.2.p.e 4
931.2.p.f 4
931.2.p.g 16
931.2.p.h 16
931.2.p.i 80
931.2.s $$\chi_{931}(31, \cdot)$$ 931.2.s.a 2 2
931.2.s.b 2
931.2.s.c 4
931.2.s.d 4
931.2.s.e 4
931.2.s.f 12
931.2.s.g 16
931.2.s.h 80
931.2.u $$\chi_{931}(134, \cdot)$$ 931.2.u.a 240 6
931.2.u.b 264
931.2.v $$\chi_{931}(177, \cdot)$$ 931.2.v.a 6 6
931.2.v.b 6
931.2.v.c 30
931.2.v.d 30
931.2.v.e 30
931.2.v.f 30
931.2.v.g 60
931.2.v.h 66
931.2.v.i 120
931.2.w $$\chi_{931}(99, \cdot)$$ 931.2.w.a 6 6
931.2.w.b 30
931.2.w.c 30
931.2.w.d 60
931.2.w.e 66
931.2.w.f 66
931.2.w.g 120
931.2.x $$\chi_{931}(226, \cdot)$$ 931.2.x.a 6 6
931.2.x.b 6
931.2.x.c 30
931.2.x.d 30
931.2.x.e 30
931.2.x.f 30
931.2.x.g 60
931.2.x.h 66
931.2.x.i 120
931.2.z $$\chi_{931}(132, \cdot)$$ 931.2.z.a 12 6
931.2.z.b 528
931.2.be $$\chi_{931}(48, \cdot)$$ 931.2.be.a 66 6
931.2.be.b 66
931.2.be.c 240
931.2.bf $$\chi_{931}(325, \cdot)$$ 931.2.bf.a 66 6
931.2.bf.b 72
931.2.bf.c 240
931.2.bj $$\chi_{931}(117, \cdot)$$ 931.2.bj.a 66 6
931.2.bj.b 72
931.2.bj.c 240
931.2.bk $$\chi_{931}(11, \cdot)$$ 931.2.bk.a 1104 12
931.2.bl $$\chi_{931}(102, \cdot)$$ 931.2.bl.a 1104 12
931.2.bm $$\chi_{931}(39, \cdot)$$ 931.2.bm.a 480 12
931.2.bm.b 528
931.2.bn $$\chi_{931}(64, \cdot)$$ 931.2.bn.a 1080 12
931.2.bp $$\chi_{931}(103, \cdot)$$ 931.2.bp.a 1104 12
931.2.bs $$\chi_{931}(27, \cdot)$$ 931.2.bs.a 1080 12
931.2.bt $$\chi_{931}(75, \cdot)$$ 931.2.bt.a 24 12
931.2.bt.b 1080
931.2.bz $$\chi_{931}(12, \cdot)$$ 931.2.bz.a 1104 12
931.2.ca $$\chi_{931}(4, \cdot)$$ 931.2.ca.a 3276 36
931.2.cb $$\chi_{931}(9, \cdot)$$ 931.2.cb.a 3276 36
931.2.cc $$\chi_{931}(36, \cdot)$$ 931.2.cc.a 3312 36
931.2.cd $$\chi_{931}(10, \cdot)$$ 931.2.cd.a 3276 36
931.2.ch $$\chi_{931}(13, \cdot)$$ 931.2.ch.a 3312 36
931.2.ci $$\chi_{931}(3, \cdot)$$ 931.2.ci.a 3276 36

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(931))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(931)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 2}$$