# Properties

 Label 570.2 Level 570 Weight 2 Dimension 1965 Nonzero newspaces 18 Newform subspaces 70 Sturm bound 34560 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Newform subspaces: $$70$$ Sturm bound: $$34560$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(570))$$.

Total New Old
Modular forms 9216 1965 7251
Cusp forms 8065 1965 6100
Eisenstein series 1151 0 1151

## Trace form

 $$1965 q + q^{2} + 5 q^{3} + q^{4} + 9 q^{5} + 5 q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10})$$ $$1965 q + q^{2} + 5 q^{3} + q^{4} + 9 q^{5} + 5 q^{6} + 8 q^{7} + q^{8} + q^{9} - 7 q^{10} - 20 q^{11} + q^{12} + 78 q^{13} + 48 q^{14} + 17 q^{15} + q^{16} + 42 q^{17} - 15 q^{18} + 153 q^{19} + 29 q^{20} + 76 q^{21} + 104 q^{22} + 48 q^{23} + 5 q^{24} + 89 q^{25} + 86 q^{26} + 35 q^{27} + 32 q^{28} + 54 q^{29} + 29 q^{30} + 72 q^{31} + q^{32} + 104 q^{33} - 14 q^{34} + 48 q^{35} + q^{36} - 18 q^{37} - 23 q^{38} + 66 q^{39} - 23 q^{40} + 34 q^{41} - 24 q^{42} + 60 q^{43} - 4 q^{44} + 9 q^{45} - 72 q^{46} + 24 q^{47} - 29 q^{48} - 15 q^{49} - 15 q^{50} - 168 q^{51} - 18 q^{52} - 42 q^{53} - 103 q^{54} - 20 q^{55} - 8 q^{56} - 179 q^{57} - 2 q^{58} - 20 q^{59} - 23 q^{60} + 22 q^{61} - 16 q^{62} - 124 q^{63} + q^{64} + 50 q^{65} - 180 q^{66} + 116 q^{67} - 30 q^{68} - 116 q^{69} + 8 q^{70} - 48 q^{71} - q^{72} + 70 q^{73} - 42 q^{74} - 31 q^{75} - 31 q^{76} - 96 q^{77} - 82 q^{78} - 72 q^{79} + 9 q^{80} - 207 q^{81} - 166 q^{82} - 252 q^{83} - 116 q^{84} - 462 q^{85} - 212 q^{86} - 274 q^{87} - 4 q^{88} - 310 q^{89} - 293 q^{90} - 336 q^{91} - 168 q^{92} - 340 q^{93} - 304 q^{94} - 347 q^{95} - 11 q^{96} - 342 q^{97} - 327 q^{98} - 418 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(570))$$

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
570.2.a $$\chi_{570}(1, \cdot)$$ 570.2.a.a 1 1
570.2.a.b 1
570.2.a.c 1
570.2.a.d 1
570.2.a.e 1
570.2.a.f 1
570.2.a.g 1
570.2.a.h 1
570.2.a.i 1
570.2.a.j 1
570.2.a.k 1
570.2.a.l 1
570.2.a.m 1
570.2.c $$\chi_{570}(569, \cdot)$$ 570.2.c.a 4 1
570.2.c.b 4
570.2.c.c 8
570.2.c.d 8
570.2.c.e 8
570.2.c.f 8
570.2.d $$\chi_{570}(229, \cdot)$$ 570.2.d.a 2 1
570.2.d.b 2
570.2.d.c 6
570.2.d.d 6
570.2.f $$\chi_{570}(341, \cdot)$$ 570.2.f.a 4 1
570.2.f.b 4
570.2.f.c 8
570.2.f.d 8
570.2.i $$\chi_{570}(121, \cdot)$$ 570.2.i.a 2 2
570.2.i.b 2
570.2.i.c 2
570.2.i.d 2
570.2.i.e 2
570.2.i.f 4
570.2.i.g 4
570.2.i.h 4
570.2.i.i 4
570.2.i.j 6
570.2.k $$\chi_{570}(77, \cdot)$$ 570.2.k.a 36 2
570.2.k.b 36
570.2.m $$\chi_{570}(37, \cdot)$$ 570.2.m.a 20 2
570.2.m.b 20
570.2.n $$\chi_{570}(179, \cdot)$$ 570.2.n.a 80 2
570.2.q $$\chi_{570}(49, \cdot)$$ 570.2.q.a 8 2
570.2.q.b 12
570.2.q.c 20
570.2.s $$\chi_{570}(221, \cdot)$$ 570.2.s.a 24 2
570.2.s.b 24
570.2.u $$\chi_{570}(61, \cdot)$$ 570.2.u.a 6 6
570.2.u.b 6
570.2.u.c 6
570.2.u.d 6
570.2.u.e 6
570.2.u.f 6
570.2.u.g 6
570.2.u.h 6
570.2.u.i 12
570.2.u.j 12
570.2.v $$\chi_{570}(83, \cdot)$$ 570.2.v.a 8 4
570.2.v.b 8
570.2.v.c 144
570.2.x $$\chi_{570}(103, \cdot)$$ 570.2.x.a 40 4
570.2.x.b 40
570.2.bb $$\chi_{570}(41, \cdot)$$ 570.2.bb.a 84 6
570.2.bb.b 84
570.2.bc $$\chi_{570}(139, \cdot)$$ 570.2.bc.a 60 6
570.2.bc.b 60
570.2.bf $$\chi_{570}(29, \cdot)$$ 570.2.bf.a 240 6
570.2.bh $$\chi_{570}(13, \cdot)$$ 570.2.bh.a 120 12
570.2.bh.b 120
570.2.bi $$\chi_{570}(17, \cdot)$$ 570.2.bi.a 480 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(570))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(570)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 2}$$