# Properties

 Label 585.2 Level 585 Weight 2 Dimension 8376 Nonzero newspaces 50 Newform subspaces 124 Sturm bound 48384 Trace bound 10

## Defining parameters

 Level: $$N$$ = $$585 = 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$50$$ Newform subspaces: $$124$$ Sturm bound: $$48384$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(585))$$.

Total New Old
Modular forms 12864 8972 3892
Cusp forms 11329 8376 2953
Eisenstein series 1535 596 939

## Trace form

 $$8376 q - 22 q^{2} - 32 q^{3} - 14 q^{4} - 36 q^{5} - 112 q^{6} - 8 q^{7} - 12 q^{8} - 40 q^{9} + O(q^{10})$$ $$8376 q - 22 q^{2} - 32 q^{3} - 14 q^{4} - 36 q^{5} - 112 q^{6} - 8 q^{7} - 12 q^{8} - 40 q^{9} - 117 q^{10} - 88 q^{11} - 64 q^{12} - 10 q^{13} - 72 q^{14} - 80 q^{15} - 54 q^{16} - 22 q^{17} - 80 q^{18} - 28 q^{19} - 71 q^{20} - 144 q^{21} + 8 q^{22} - 36 q^{23} - 168 q^{24} - 54 q^{25} - 62 q^{26} - 128 q^{27} - 88 q^{28} - 122 q^{29} - 184 q^{30} - 152 q^{31} - 218 q^{32} - 136 q^{33} - 160 q^{34} - 116 q^{35} - 272 q^{36} - 190 q^{37} - 256 q^{38} - 112 q^{39} - 182 q^{40} - 110 q^{41} - 120 q^{42} + 8 q^{43} - 128 q^{44} - 76 q^{45} - 268 q^{46} - 16 q^{47} - 112 q^{48} - 38 q^{49} - 55 q^{50} - 160 q^{51} - 20 q^{52} - 28 q^{53} - 40 q^{54} - 192 q^{55} - 264 q^{56} - 80 q^{57} - 46 q^{58} - 112 q^{59} - 172 q^{60} - 94 q^{61} - 324 q^{62} - 264 q^{63} - 452 q^{64} - 275 q^{65} - 704 q^{66} - 260 q^{67} - 734 q^{68} - 312 q^{69} - 468 q^{70} - 548 q^{71} - 408 q^{72} - 424 q^{73} - 566 q^{74} - 176 q^{75} - 620 q^{76} - 336 q^{77} - 464 q^{78} - 168 q^{79} - 377 q^{80} - 256 q^{81} - 318 q^{82} - 216 q^{83} - 240 q^{84} - 141 q^{85} - 280 q^{86} - 152 q^{87} - 264 q^{88} - 20 q^{90} - 272 q^{91} - 72 q^{92} - 72 q^{93} - 28 q^{94} + 38 q^{95} + 280 q^{96} + 80 q^{97} + 178 q^{98} + 136 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(585))$$

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
585.2.a $$\chi_{585}(1, \cdot)$$ 585.2.a.a 1 1
585.2.a.b 1
585.2.a.c 1
585.2.a.d 1
585.2.a.e 1
585.2.a.f 1
585.2.a.g 1
585.2.a.h 1
585.2.a.i 1
585.2.a.j 2
585.2.a.k 2
585.2.a.l 2
585.2.a.m 2
585.2.a.n 3
585.2.b $$\chi_{585}(181, \cdot)$$ 585.2.b.a 2 1
585.2.b.b 2
585.2.b.c 2
585.2.b.d 2
585.2.b.e 4
585.2.b.f 4
585.2.b.g 6
585.2.c $$\chi_{585}(469, \cdot)$$ 585.2.c.a 2 1
585.2.c.b 6
585.2.c.c 10
585.2.c.d 12
585.2.h $$\chi_{585}(64, \cdot)$$ 585.2.h.a 2 1
585.2.h.b 2
585.2.h.c 2
585.2.h.d 2
585.2.h.e 4
585.2.h.f 8
585.2.h.g 12
585.2.i $$\chi_{585}(196, \cdot)$$ 585.2.i.a 2 2
585.2.i.b 2
585.2.i.c 2
585.2.i.d 2
585.2.i.e 16
585.2.i.f 16
585.2.i.g 26
585.2.i.h 30
585.2.j $$\chi_{585}(406, \cdot)$$ 585.2.j.a 2 2
585.2.j.b 2
585.2.j.c 4
585.2.j.d 4
585.2.j.e 4
585.2.j.f 6
585.2.j.g 6
585.2.j.h 10
585.2.j.i 10
585.2.k $$\chi_{585}(61, \cdot)$$ 585.2.k.a 56 2
585.2.k.b 56
585.2.l $$\chi_{585}(16, \cdot)$$ 585.2.l.a 56 2
585.2.l.b 56
585.2.n $$\chi_{585}(307, \cdot)$$ 585.2.n.a 2 2
585.2.n.b 2
585.2.n.c 2
585.2.n.d 4
585.2.n.e 8
585.2.n.f 20
585.2.n.g 28
585.2.p $$\chi_{585}(53, \cdot)$$ 585.2.p.a 24 2
585.2.p.b 24
585.2.q $$\chi_{585}(44, \cdot)$$ 585.2.q.a 56 2
585.2.r $$\chi_{585}(161, \cdot)$$ 585.2.r.a 8 2
585.2.r.b 8
585.2.r.c 16
585.2.v $$\chi_{585}(233, \cdot)$$ 585.2.v.a 56 2
585.2.w $$\chi_{585}(73, \cdot)$$ 585.2.w.a 2 2
585.2.w.b 2
585.2.w.c 2
585.2.w.d 4
585.2.w.e 8
585.2.w.f 20
585.2.w.g 28
585.2.ba $$\chi_{585}(121, \cdot)$$ 585.2.ba.a 112 2
585.2.bb $$\chi_{585}(139, \cdot)$$ 585.2.bb.a 160 2
585.2.be $$\chi_{585}(259, \cdot)$$ 585.2.be.a 160 2
585.2.bf $$\chi_{585}(199, \cdot)$$ 585.2.bf.a 8 2
585.2.bf.b 24
585.2.bf.c 32
585.2.bk $$\chi_{585}(49, \cdot)$$ 585.2.bk.a 160 2
585.2.bl $$\chi_{585}(94, \cdot)$$ 585.2.bl.a 160 2
585.2.bm $$\chi_{585}(166, \cdot)$$ 585.2.bm.a 112 2
585.2.br $$\chi_{585}(79, \cdot)$$ 585.2.br.a 144 2
585.2.bs $$\chi_{585}(289, \cdot)$$ 585.2.bs.a 12 2
585.2.bs.b 24
585.2.bs.c 32
585.2.bt $$\chi_{585}(376, \cdot)$$ 585.2.bt.a 4 2
585.2.bt.b 108
585.2.bu $$\chi_{585}(316, \cdot)$$ 585.2.bu.a 4 2
585.2.bu.b 8
585.2.bu.c 8
585.2.bu.d 8
585.2.bu.e 20
585.2.bx $$\chi_{585}(4, \cdot)$$ 585.2.bx.a 160 2
585.2.ca $$\chi_{585}(58, \cdot)$$ 585.2.ca.a 320 4
585.2.cc $$\chi_{585}(67, \cdot)$$ 585.2.cc.a 320 4
585.2.cf $$\chi_{585}(163, \cdot)$$ 585.2.cf.a 20 4
585.2.cf.b 56
585.2.cf.c 56
585.2.cg $$\chi_{585}(187, \cdot)$$ 585.2.cg.a 320 4
585.2.ci $$\chi_{585}(113, \cdot)$$ 585.2.ci.a 320 4
585.2.cm $$\chi_{585}(11, \cdot)$$ 585.2.cm.a 224 4
585.2.cn $$\chi_{585}(59, \cdot)$$ 585.2.cn.a 320 4
585.2.co $$\chi_{585}(212, \cdot)$$ 585.2.co.a 320 4
585.2.cr $$\chi_{585}(23, \cdot)$$ 585.2.cr.a 320 4
585.2.cs $$\chi_{585}(38, \cdot)$$ 585.2.cs.a 320 4
585.2.cv $$\chi_{585}(17, \cdot)$$ 585.2.cv.a 112 4
585.2.cw $$\chi_{585}(71, \cdot)$$ 585.2.cw.a 40 4
585.2.cw.b 40
585.2.cx $$\chi_{585}(89, \cdot)$$ 585.2.cx.a 112 4
585.2.dc $$\chi_{585}(164, \cdot)$$ 585.2.dc.a 320 4
585.2.dd $$\chi_{585}(41, \cdot)$$ 585.2.dd.a 224 4
585.2.de $$\chi_{585}(254, \cdot)$$ 585.2.de.a 320 4
585.2.df $$\chi_{585}(86, \cdot)$$ 585.2.df.a 224 4
585.2.dj $$\chi_{585}(92, \cdot)$$ 585.2.dj.a 288 4
585.2.dk $$\chi_{585}(68, \cdot)$$ 585.2.dk.a 320 4
585.2.dn $$\chi_{585}(107, \cdot)$$ 585.2.dn.a 112 4
585.2.dp $$\chi_{585}(28, \cdot)$$ 585.2.dp.a 20 4
585.2.dp.b 56
585.2.dp.c 56
585.2.dq $$\chi_{585}(112, \cdot)$$ 585.2.dq.a 320 4
585.2.dt $$\chi_{585}(7, \cdot)$$ 585.2.dt.a 320 4
585.2.dv $$\chi_{585}(292, \cdot)$$ 585.2.dv.a 320 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(585))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(585)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(585))$$$$^{\oplus 1}$$