# Properties

 Label 825.2 Level 825 Weight 2 Dimension 15942 Nonzero newspaces 42 Newform subspaces 148 Sturm bound 96000 Trace bound 10

## Defining parameters

 Level: $$N$$ = $$825 = 3 \cdot 5^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$42$$ Newform subspaces: $$148$$ Sturm bound: $$96000$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(825))$$.

Total New Old
Modular forms 25120 16682 8438
Cusp forms 22881 15942 6939
Eisenstein series 2239 740 1499

## Trace form

 $$15942 q + 2 q^{2} - 47 q^{3} - 80 q^{4} + 12 q^{5} - 54 q^{6} - 64 q^{7} + 62 q^{8} - 29 q^{9} + O(q^{10})$$ $$15942 q + 2 q^{2} - 47 q^{3} - 80 q^{4} + 12 q^{5} - 54 q^{6} - 64 q^{7} + 62 q^{8} - 29 q^{9} - 92 q^{10} + 14 q^{11} - 72 q^{12} - 60 q^{13} + 78 q^{14} - 52 q^{15} - 84 q^{16} + 34 q^{17} - 48 q^{18} - 84 q^{19} - 72 q^{20} - 68 q^{21} - 86 q^{22} - 12 q^{23} - 142 q^{24} - 188 q^{25} + 62 q^{26} - 62 q^{27} - 168 q^{28} - 8 q^{29} - 108 q^{30} - 134 q^{31} - 14 q^{32} - 65 q^{33} - 180 q^{34} + 40 q^{35} - 118 q^{36} - 34 q^{37} + 34 q^{38} - 64 q^{39} - 324 q^{40} + 104 q^{41} - 242 q^{42} - 236 q^{43} - 258 q^{44} - 288 q^{45} - 424 q^{46} - 202 q^{47} - 444 q^{48} - 514 q^{49} - 372 q^{50} - 346 q^{51} - 836 q^{52} - 282 q^{53} - 400 q^{54} - 324 q^{55} - 520 q^{56} - 346 q^{57} - 732 q^{58} - 266 q^{59} - 268 q^{60} - 372 q^{61} - 268 q^{62} - 104 q^{63} - 468 q^{64} - 4 q^{65} - 212 q^{66} - 226 q^{67} + 24 q^{68} + 73 q^{69} + 40 q^{70} + 172 q^{71} + 272 q^{72} + 188 q^{73} + 358 q^{74} + 148 q^{75} + 28 q^{76} + 186 q^{77} + 156 q^{78} + 200 q^{79} + 308 q^{80} + 27 q^{81} + 72 q^{82} + 186 q^{83} + 52 q^{84} - 236 q^{85} + 148 q^{86} + 28 q^{87} - 34 q^{88} - 64 q^{89} - 212 q^{90} - 284 q^{91} - 294 q^{92} - 361 q^{93} - 884 q^{94} - 272 q^{95} - 666 q^{96} - 806 q^{97} - 850 q^{98} - 431 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(825))$$

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
825.2.a $$\chi_{825}(1, \cdot)$$ 825.2.a.a 1 1
825.2.a.b 1
825.2.a.c 1
825.2.a.d 2
825.2.a.e 2
825.2.a.f 2
825.2.a.g 2
825.2.a.h 3
825.2.a.i 3
825.2.a.j 3
825.2.a.k 3
825.2.a.l 3
825.2.a.m 3
825.2.a.n 3
825.2.c $$\chi_{825}(199, \cdot)$$ 825.2.c.a 2 1
825.2.c.b 2
825.2.c.c 4
825.2.c.d 4
825.2.c.e 4
825.2.c.f 6
825.2.c.g 6
825.2.d $$\chi_{825}(824, \cdot)$$ 825.2.d.a 4 1
825.2.d.b 8
825.2.d.c 8
825.2.d.d 8
825.2.d.e 8
825.2.d.f 32
825.2.f $$\chi_{825}(626, \cdot)$$ 825.2.f.a 2 1
825.2.f.b 4
825.2.f.c 8
825.2.f.d 8
825.2.f.e 16
825.2.f.f 16
825.2.f.g 16
825.2.j $$\chi_{825}(43, \cdot)$$ 825.2.j.a 8 2
825.2.j.b 8
825.2.j.c 24
825.2.j.d 32
825.2.k $$\chi_{825}(518, \cdot)$$ 825.2.k.a 4 2
825.2.k.b 4
825.2.k.c 4
825.2.k.d 4
825.2.k.e 4
825.2.k.f 4
825.2.k.g 4
825.2.k.h 4
825.2.k.i 16
825.2.k.j 16
825.2.k.k 28
825.2.k.l 28
825.2.m $$\chi_{825}(16, \cdot)$$ 825.2.m.a 4 4
825.2.m.b 4
825.2.m.c 116
825.2.m.d 116
825.2.n $$\chi_{825}(301, \cdot)$$ 825.2.n.a 4 4
825.2.n.b 4
825.2.n.c 4
825.2.n.d 4
825.2.n.e 4
825.2.n.f 4
825.2.n.g 8
825.2.n.h 8
825.2.n.i 8
825.2.n.j 8
825.2.n.k 8
825.2.n.l 8
825.2.n.m 16
825.2.n.n 16
825.2.n.o 24
825.2.n.p 24
825.2.o $$\chi_{825}(421, \cdot)$$ 825.2.o.a 4 4
825.2.o.b 4
825.2.o.c 116
825.2.o.d 116
825.2.p $$\chi_{825}(181, \cdot)$$ 825.2.p.a 4 4
825.2.p.b 116
825.2.p.c 120
825.2.q $$\chi_{825}(166, \cdot)$$ 825.2.q.a 48 4
825.2.q.b 48
825.2.q.c 48
825.2.q.d 48
825.2.r $$\chi_{825}(31, \cdot)$$ 825.2.r.a 4 4
825.2.r.b 116
825.2.r.c 120
825.2.s $$\chi_{825}(479, \cdot)$$ 825.2.s.a 464 4
825.2.v $$\chi_{825}(379, \cdot)$$ 825.2.v.a 240 4
825.2.x $$\chi_{825}(131, \cdot)$$ 825.2.x.a 8 4
825.2.x.b 8
825.2.x.c 448
825.2.bd $$\chi_{825}(281, \cdot)$$ 825.2.bd.a 464 4
825.2.bf $$\chi_{825}(266, \cdot)$$ 825.2.bf.a 464 4
825.2.bi $$\chi_{825}(101, \cdot)$$ 825.2.bi.a 8 4
825.2.bi.b 8
825.2.bi.c 8
825.2.bi.d 16
825.2.bi.e 48
825.2.bi.f 56
825.2.bi.g 56
825.2.bi.h 80
825.2.bj $$\chi_{825}(116, \cdot)$$ 825.2.bj.a 464 4
825.2.bl $$\chi_{825}(34, \cdot)$$ 825.2.bl.a 104 4
825.2.bl.b 104
825.2.bo $$\chi_{825}(134, \cdot)$$ 825.2.bo.a 464 4
825.2.br $$\chi_{825}(29, \cdot)$$ 825.2.br.a 464 4
825.2.bs $$\chi_{825}(74, \cdot)$$ 825.2.bs.a 8 4
825.2.bs.b 8
825.2.bs.c 8
825.2.bs.d 8
825.2.bs.e 16
825.2.bs.f 16
825.2.bs.g 48
825.2.bs.h 48
825.2.bs.i 112
825.2.bu $$\chi_{825}(239, \cdot)$$ 825.2.bu.a 464 4
825.2.bv $$\chi_{825}(229, \cdot)$$ 825.2.bv.a 240 4
825.2.bx $$\chi_{825}(49, \cdot)$$ 825.2.bx.a 8 4
825.2.bx.b 8
825.2.bx.c 8
825.2.bx.d 8
825.2.bx.e 16
825.2.bx.f 16
825.2.bx.g 16
825.2.bx.h 16
825.2.bx.i 16
825.2.bx.j 32
825.2.by $$\chi_{825}(4, \cdot)$$ 825.2.by.a 240 4
825.2.cb $$\chi_{825}(169, \cdot)$$ 825.2.cb.a 240 4
825.2.ce $$\chi_{825}(164, \cdot)$$ 825.2.ce.a 8 4
825.2.ce.b 8
825.2.ce.c 448
825.2.cg $$\chi_{825}(41, \cdot)$$ 825.2.cg.a 464 4
825.2.ci $$\chi_{825}(113, \cdot)$$ 825.2.ci.a 928 8
825.2.cl $$\chi_{825}(28, \cdot)$$ 825.2.cl.a 480 8
825.2.cm $$\chi_{825}(13, \cdot)$$ 825.2.cm.a 480 8
825.2.cs $$\chi_{825}(23, \cdot)$$ 825.2.cs.a 400 8
825.2.cs.b 400
825.2.ct $$\chi_{825}(218, \cdot)$$ 825.2.ct.a 128 8
825.2.ct.b 160
825.2.ct.c 256
825.2.cu $$\chi_{825}(53, \cdot)$$ 825.2.cu.a 928 8
825.2.cv $$\chi_{825}(38, \cdot)$$ 825.2.cv.a 928 8
825.2.cw $$\chi_{825}(7, \cdot)$$ 825.2.cw.a 64 8
825.2.cw.b 96
825.2.cw.c 128
825.2.cx $$\chi_{825}(52, \cdot)$$ 825.2.cx.a 480 8
825.2.cy $$\chi_{825}(172, \cdot)$$ 825.2.cy.a 480 8
825.2.cz $$\chi_{825}(142, \cdot)$$ 825.2.cz.a 480 8
825.2.df $$\chi_{825}(47, \cdot)$$ 825.2.df.a 928 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(825))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(825)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 2}$$