# Properties

 Label 567.2 Level 567 Weight 2 Dimension 8552 Nonzero newspaces 22 Newform subspaces 98 Sturm bound 46656 Trace bound 21

## Defining parameters

 Level: $$N$$ = $$567 = 3^{4} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$22$$ Newform subspaces: $$98$$ Sturm bound: $$46656$$ Trace bound: $$21$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(567))$$.

Total New Old
Modular forms 12312 9112 3200
Cusp forms 11017 8552 2465
Eisenstein series 1295 560 735

## Trace form

 $$8552 q - 48 q^{2} - 72 q^{3} - 76 q^{4} - 42 q^{5} - 72 q^{6} - 97 q^{7} - 96 q^{8} - 72 q^{9} + O(q^{10})$$ $$8552 q - 48 q^{2} - 72 q^{3} - 76 q^{4} - 42 q^{5} - 72 q^{6} - 97 q^{7} - 96 q^{8} - 72 q^{9} - 96 q^{10} - 30 q^{11} - 72 q^{12} - 62 q^{13} - 39 q^{14} - 180 q^{15} - 76 q^{16} - 18 q^{17} - 90 q^{18} - 128 q^{19} - 114 q^{20} - 117 q^{21} - 210 q^{22} - 114 q^{23} - 180 q^{24} - 100 q^{25} - 222 q^{26} - 126 q^{27} - 169 q^{28} - 174 q^{29} - 180 q^{30} - 98 q^{31} - 144 q^{32} - 126 q^{33} - 102 q^{34} - 69 q^{35} - 252 q^{36} - 92 q^{37} + 30 q^{38} - 72 q^{39} - 150 q^{40} - 42 q^{41} - 135 q^{42} - 194 q^{43} - 174 q^{44} - 180 q^{45} - 204 q^{46} - 174 q^{47} - 270 q^{48} - 145 q^{49} - 480 q^{50} - 198 q^{51} - 230 q^{52} - 288 q^{53} - 324 q^{54} - 276 q^{55} - 411 q^{56} - 288 q^{57} - 234 q^{58} - 276 q^{59} - 306 q^{60} - 164 q^{61} - 420 q^{62} - 144 q^{63} - 460 q^{64} - 192 q^{65} - 72 q^{66} - 152 q^{67} - 72 q^{68} + 36 q^{69} - 249 q^{70} + 18 q^{71} + 360 q^{72} - 110 q^{73} + 210 q^{74} + 108 q^{75} - 194 q^{76} + 51 q^{77} + 54 q^{78} - 92 q^{79} + 444 q^{80} + 72 q^{81} - 120 q^{82} + 186 q^{83} + 135 q^{84} - 258 q^{85} + 354 q^{86} + 216 q^{87} - 234 q^{88} + 108 q^{89} + 90 q^{90} - 140 q^{91} + 66 q^{92} - 108 q^{93} - 162 q^{94} - 174 q^{95} - 54 q^{96} - 182 q^{97} - 219 q^{98} - 324 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(567))$$

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
567.2.a $$\chi_{567}(1, \cdot)$$ 567.2.a.a 1 1
567.2.a.b 1
567.2.a.c 3
567.2.a.d 3
567.2.a.e 3
567.2.a.f 3
567.2.a.g 3
567.2.a.h 3
567.2.a.i 4
567.2.c $$\chi_{567}(566, \cdot)$$ 567.2.c.a 8 1
567.2.c.b 8
567.2.c.c 12
567.2.e $$\chi_{567}(163, \cdot)$$ 567.2.e.a 2 2
567.2.e.b 2
567.2.e.c 8
567.2.e.d 8
567.2.e.e 10
567.2.e.f 10
567.2.e.g 16
567.2.f $$\chi_{567}(190, \cdot)$$ 567.2.f.a 2 2
567.2.f.b 2
567.2.f.c 2
567.2.f.d 2
567.2.f.e 2
567.2.f.f 2
567.2.f.g 2
567.2.f.h 2
567.2.f.i 4
567.2.f.j 4
567.2.f.k 4
567.2.f.l 6
567.2.f.m 6
567.2.f.n 8
567.2.g $$\chi_{567}(109, \cdot)$$ 567.2.g.a 2 2
567.2.g.b 2
567.2.g.c 2
567.2.g.d 2
567.2.g.e 2
567.2.g.f 2
567.2.g.g 4
567.2.g.h 6
567.2.g.i 6
567.2.g.j 8
567.2.g.k 8
567.2.g.l 16
567.2.h $$\chi_{567}(298, \cdot)$$ 567.2.h.a 2 2
567.2.h.b 2
567.2.h.c 2
567.2.h.d 2
567.2.h.e 2
567.2.h.f 2
567.2.h.g 4
567.2.h.h 6
567.2.h.i 6
567.2.h.j 8
567.2.h.k 8
567.2.h.l 16
567.2.i $$\chi_{567}(215, \cdot)$$ 567.2.i.a 2 2
567.2.i.b 2
567.2.i.c 4
567.2.i.d 4
567.2.i.e 4
567.2.i.f 12
567.2.i.g 32
567.2.o $$\chi_{567}(188, \cdot)$$ 567.2.o.a 2 2
567.2.o.b 2
567.2.o.c 4
567.2.o.d 4
567.2.o.e 8
567.2.o.f 8
567.2.o.g 16
567.2.o.h 16
567.2.p $$\chi_{567}(80, \cdot)$$ 567.2.p.a 2 2
567.2.p.b 2
567.2.p.c 10
567.2.p.d 10
567.2.p.e 32
567.2.s $$\chi_{567}(26, \cdot)$$ 567.2.s.a 2 2
567.2.s.b 2
567.2.s.c 4
567.2.s.d 4
567.2.s.e 4
567.2.s.f 12
567.2.s.g 32
567.2.u $$\chi_{567}(100, \cdot)$$ 567.2.u.a 132 6
567.2.v $$\chi_{567}(64, \cdot)$$ 567.2.v.a 54 6
567.2.v.b 54
567.2.w $$\chi_{567}(37, \cdot)$$ 567.2.w.a 132 6
567.2.ba $$\chi_{567}(143, \cdot)$$ 567.2.ba.a 132 6
567.2.bd $$\chi_{567}(17, \cdot)$$ 567.2.bd.a 132 6
567.2.be $$\chi_{567}(62, \cdot)$$ 567.2.be.a 132 6
567.2.bg $$\chi_{567}(4, \cdot)$$ 567.2.bg.a 1260 18
567.2.bh $$\chi_{567}(22, \cdot)$$ 567.2.bh.a 486 18
567.2.bh.b 486
567.2.bi $$\chi_{567}(25, \cdot)$$ 567.2.bi.a 1260 18
567.2.bl $$\chi_{567}(47, \cdot)$$ 567.2.bl.a 1260 18
567.2.bm $$\chi_{567}(20, \cdot)$$ 567.2.bm.a 1260 18
567.2.br $$\chi_{567}(5, \cdot)$$ 567.2.br.a 1260 18

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(567))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(567)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(189))$$$$^{\oplus 2}$$