# Properties

 Label 855.2 Level 855 Weight 2 Dimension 18246 Nonzero newspaces 48 Newform subspaces 126 Sturm bound 103680 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$855 = 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Newform subspaces: $$126$$ Sturm bound: $$103680$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(855))$$.

Total New Old
Modular forms 27072 19166 7906
Cusp forms 24769 18246 6523
Eisenstein series 2303 920 1383

## Trace form

 $$18246 q - 40 q^{2} - 56 q^{3} - 32 q^{4} - 63 q^{5} - 184 q^{6} - 30 q^{7} - 48 q^{8} - 64 q^{9} + O(q^{10})$$ $$18246 q - 40 q^{2} - 56 q^{3} - 32 q^{4} - 63 q^{5} - 184 q^{6} - 30 q^{7} - 48 q^{8} - 64 q^{9} - 213 q^{10} - 154 q^{11} - 88 q^{12} - 26 q^{13} - 42 q^{14} - 116 q^{15} - 76 q^{16} - 40 q^{17} - 104 q^{18} - 100 q^{19} - 176 q^{20} - 216 q^{21} - 16 q^{22} - 60 q^{23} - 144 q^{24} - 69 q^{25} - 154 q^{26} - 104 q^{27} - 100 q^{28} - 62 q^{29} - 172 q^{30} - 110 q^{31} + 10 q^{32} - 88 q^{33} + 8 q^{34} - 29 q^{35} - 224 q^{36} - 112 q^{37} + 88 q^{38} - 80 q^{39} + 46 q^{40} - 26 q^{41} + 64 q^{43} + 10 q^{44} - 106 q^{45} - 532 q^{46} - 100 q^{47} - 244 q^{48} - 150 q^{49} - 208 q^{50} - 364 q^{51} - 454 q^{52} - 274 q^{53} - 280 q^{54} - 375 q^{55} - 912 q^{56} - 268 q^{57} - 376 q^{58} - 412 q^{59} - 364 q^{60} - 370 q^{61} - 456 q^{62} - 336 q^{63} - 512 q^{64} - 286 q^{65} - 680 q^{66} - 84 q^{67} - 446 q^{68} - 300 q^{69} - 201 q^{70} - 380 q^{71} - 228 q^{72} - 14 q^{73} - 14 q^{74} - 92 q^{75} - 18 q^{76} + 78 q^{77} + 8 q^{78} + 102 q^{79} - 209 q^{80} - 136 q^{81} + 96 q^{82} + 108 q^{83} + 72 q^{84} - 105 q^{85} + 92 q^{86} + 16 q^{87} - 90 q^{88} + 132 q^{89} + 10 q^{90} - 366 q^{91} + 84 q^{92} + 48 q^{93} - 280 q^{94} - 230 q^{95} - 608 q^{96} - 328 q^{97} - 626 q^{98} - 284 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(855))$$

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
855.2.a $$\chi_{855}(1, \cdot)$$ 855.2.a.a 1 1
855.2.a.b 1
855.2.a.c 1
855.2.a.d 2
855.2.a.e 2
855.2.a.f 2
855.2.a.g 2
855.2.a.h 3
855.2.a.i 3
855.2.a.j 3
855.2.a.k 3
855.2.a.l 3
855.2.a.m 4
855.2.b $$\chi_{855}(854, \cdot)$$ 855.2.b.a 4 1
855.2.b.b 4
855.2.b.c 8
855.2.b.d 24
855.2.c $$\chi_{855}(514, \cdot)$$ 855.2.c.a 2 1
855.2.c.b 2
855.2.c.c 2
855.2.c.d 6
855.2.c.e 6
855.2.c.f 12
855.2.c.g 14
855.2.h $$\chi_{855}(341, \cdot)$$ 855.2.h.a 24 1
855.2.i $$\chi_{855}(286, \cdot)$$ 855.2.i.a 26 2
855.2.i.b 30
855.2.i.c 42
855.2.i.d 46
855.2.j $$\chi_{855}(106, \cdot)$$ 855.2.j.a 80 2
855.2.j.b 80
855.2.k $$\chi_{855}(406, \cdot)$$ 855.2.k.a 2 2
855.2.k.b 2
855.2.k.c 2
855.2.k.d 2
855.2.k.e 4
855.2.k.f 4
855.2.k.g 6
855.2.k.h 8
855.2.k.i 10
855.2.k.j 12
855.2.k.k 12
855.2.l $$\chi_{855}(391, \cdot)$$ 855.2.l.a 80 2
855.2.l.b 80
855.2.n $$\chi_{855}(647, \cdot)$$ 855.2.n.a 4 2
855.2.n.b 4
855.2.n.c 8
855.2.n.d 20
855.2.n.e 36
855.2.p $$\chi_{855}(37, \cdot)$$ 855.2.p.a 4 2
855.2.p.b 4
855.2.p.c 4
855.2.p.d 4
855.2.p.e 8
855.2.p.f 12
855.2.p.g 24
855.2.p.h 36
855.2.s $$\chi_{855}(49, \cdot)$$ 855.2.s.a 232 2
855.2.t $$\chi_{855}(164, \cdot)$$ 855.2.t.a 232 2
855.2.w $$\chi_{855}(56, \cdot)$$ 855.2.w.a 160 2
855.2.x $$\chi_{855}(221, \cdot)$$ 855.2.x.a 160 2
855.2.bc $$\chi_{855}(521, \cdot)$$ 855.2.bc.a 48 2
855.2.bd $$\chi_{855}(179, \cdot)$$ 855.2.bd.a 16 2
855.2.bd.b 64
855.2.be $$\chi_{855}(64, \cdot)$$ 855.2.be.a 4 2
855.2.be.b 8
855.2.be.c 8
855.2.be.d 12
855.2.be.e 24
855.2.be.f 40
855.2.bj $$\chi_{855}(229, \cdot)$$ 855.2.bj.a 108 2
855.2.bj.b 108
855.2.bk $$\chi_{855}(619, \cdot)$$ 855.2.bk.a 232 2
855.2.bl $$\chi_{855}(284, \cdot)$$ 855.2.bl.a 32 2
855.2.bl.b 200
855.2.bm $$\chi_{855}(734, \cdot)$$ 855.2.bm.a 232 2
855.2.bp $$\chi_{855}(506, \cdot)$$ 855.2.bp.a 160 2
855.2.bs $$\chi_{855}(226, \cdot)$$ 855.2.bs.a 12 6
855.2.bs.b 18
855.2.bs.c 18
855.2.bs.d 18
855.2.bs.e 24
855.2.bs.f 30
855.2.bs.g 42
855.2.bs.h 42
855.2.bt $$\chi_{855}(61, \cdot)$$ 855.2.bt.a 240 6
855.2.bt.b 240
855.2.bu $$\chi_{855}(16, \cdot)$$ 855.2.bu.a 240 6
855.2.bu.b 240
855.2.bv $$\chi_{855}(88, \cdot)$$ 855.2.bv.a 464 4
855.2.bx $$\chi_{855}(68, \cdot)$$ 855.2.bx.a 464 4
855.2.bz $$\chi_{855}(197, \cdot)$$ 855.2.bz.a 160 4
855.2.cc $$\chi_{855}(322, \cdot)$$ 855.2.cc.a 464 4
855.2.ce $$\chi_{855}(202, \cdot)$$ 855.2.ce.a 464 4
855.2.cg $$\chi_{855}(77, \cdot)$$ 855.2.cg.a 4 4
855.2.cg.b 4
855.2.cg.c 208
855.2.cg.d 216
855.2.ci $$\chi_{855}(182, \cdot)$$ 855.2.ci.a 464 4
855.2.cj $$\chi_{855}(217, \cdot)$$ 855.2.cj.a 4 4
855.2.cj.b 4
855.2.cj.c 4
855.2.cj.d 4
855.2.cj.e 24
855.2.cj.f 72
855.2.cj.g 80
855.2.cn $$\chi_{855}(4, \cdot)$$ 855.2.cn.a 696 6
855.2.co $$\chi_{855}(299, \cdot)$$ 855.2.co.a 696 6
855.2.cp $$\chi_{855}(41, \cdot)$$ 855.2.cp.a 480 6
855.2.cq $$\chi_{855}(71, \cdot)$$ 855.2.cq.a 168 6
855.2.cz $$\chi_{855}(14, \cdot)$$ 855.2.cz.a 696 6
855.2.da $$\chi_{855}(199, \cdot)$$ 855.2.da.a 24 6
855.2.da.b 48
855.2.da.c 96
855.2.da.d 120
855.2.db $$\chi_{855}(89, \cdot)$$ 855.2.db.a 240 6
855.2.dc $$\chi_{855}(454, \cdot)$$ 855.2.dc.a 696 6
855.2.dd $$\chi_{855}(86, \cdot)$$ 855.2.dd.a 480 6
855.2.dh $$\chi_{855}(47, \cdot)$$ 855.2.dh.a 1392 12
855.2.dk $$\chi_{855}(13, \cdot)$$ 855.2.dk.a 1392 12
855.2.dl $$\chi_{855}(127, \cdot)$$ 855.2.dl.a 96 12
855.2.dl.b 240
855.2.dl.c 240
855.2.dm $$\chi_{855}(23, \cdot)$$ 855.2.dm.a 1392 12
855.2.dn $$\chi_{855}(17, \cdot)$$ 855.2.dn.a 480 12
855.2.dq $$\chi_{855}(22, \cdot)$$ 855.2.dq.a 1392 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(855))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(855)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 2}$$