# Properties

 Label 570.4 Level 570 Weight 4 Dimension 5908 Nonzero newspaces 18 Sturm bound 69120 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$18$$ Sturm bound: $$69120$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(570))$$.

Total New Old
Modular forms 26496 5908 20588
Cusp forms 25344 5908 19436
Eisenstein series 1152 0 1152

## Trace form

 $$5908q - 28q^{3} - 8q^{5} + 8q^{6} - 80q^{7} + O(q^{10})$$ $$5908q - 28q^{3} - 8q^{5} + 8q^{6} - 80q^{7} + 80q^{10} - 64q^{11} + 304q^{12} + 1456q^{13} + 272q^{14} + 260q^{15} + 256q^{16} - 1008q^{17} + 32q^{18} - 3040q^{19} - 544q^{20} - 2128q^{21} - 1320q^{22} - 96q^{24} + 1088q^{25} + 2160q^{26} + 3230q^{27} + 1408q^{28} + 2952q^{29} - 168q^{30} + 456q^{31} - 2764q^{33} + 448q^{34} - 2680q^{35} - 1024q^{36} - 3800q^{37} - 432q^{38} - 4236q^{39} + 192q^{40} - 1048q^{41} + 2176q^{42} + 4288q^{43} + 1984q^{44} - 350q^{45} + 2816q^{46} + 4104q^{47} - 224q^{48} + 4776q^{49} + 352q^{50} + 6946q^{51} - 704q^{52} - 288q^{53} + 5184q^{54} - 3584q^{55} + 640q^{56} + 8920q^{57} - 5376q^{58} - 3280q^{59} - 736q^{60} + 2120q^{61} - 2016q^{62} - 52q^{63} - 756q^{65} - 5248q^{66} + 256q^{67} + 576q^{68} - 10032q^{69} + 5760q^{70} - 504q^{71} - 3440q^{72} - 8348q^{73} - 160q^{74} + 1552q^{75} + 704q^{76} - 17064q^{77} - 5088q^{78} - 27464q^{79} - 128q^{80} - 4688q^{81} - 11616q^{82} - 7272q^{83} - 2304q^{84} + 2944q^{85} + 256q^{86} + 6512q^{87} - 2688q^{88} + 18712q^{89} + 9212q^{90} + 33920q^{91} + 12096q^{92} + 27860q^{93} + 22208q^{94} + 31632q^{95} + 640q^{96} + 36880q^{97} + 27648q^{98} + 13554q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(570))$$

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
570.4.a $$\chi_{570}(1, \cdot)$$ 570.4.a.a 1 1
570.4.a.b 1
570.4.a.c 1
570.4.a.d 1
570.4.a.e 1
570.4.a.f 1
570.4.a.g 1
570.4.a.h 2
570.4.a.i 2
570.4.a.j 2
570.4.a.k 2
570.4.a.l 2
570.4.a.m 2
570.4.a.n 2
570.4.a.o 2
570.4.a.p 3
570.4.a.q 3
570.4.a.r 3
570.4.a.s 4
570.4.c $$\chi_{570}(569, \cdot)$$ n/a 120 1
570.4.d $$\chi_{570}(229, \cdot)$$ 570.4.d.a 2 1
570.4.d.b 2
570.4.d.c 8
570.4.d.d 12
570.4.d.e 14
570.4.d.f 18
570.4.f $$\chi_{570}(341, \cdot)$$ 570.4.f.a 40 1
570.4.f.b 40
570.4.i $$\chi_{570}(121, \cdot)$$ 570.4.i.a 2 2
570.4.i.b 2
570.4.i.c 2
570.4.i.d 2
570.4.i.e 2
570.4.i.f 2
570.4.i.g 2
570.4.i.h 4
570.4.i.i 4
570.4.i.j 6
570.4.i.k 8
570.4.i.l 10
570.4.i.m 10
570.4.i.n 12
570.4.i.o 12
570.4.k $$\chi_{570}(77, \cdot)$$ n/a 216 2
570.4.m $$\chi_{570}(37, \cdot)$$ n/a 120 2
570.4.n $$\chi_{570}(179, \cdot)$$ n/a 240 2
570.4.q $$\chi_{570}(49, \cdot)$$ n/a 120 2
570.4.s $$\chi_{570}(221, \cdot)$$ n/a 160 2
570.4.u $$\chi_{570}(61, \cdot)$$ n/a 240 6
570.4.v $$\chi_{570}(83, \cdot)$$ n/a 480 4
570.4.x $$\chi_{570}(103, \cdot)$$ n/a 240 4
570.4.bb $$\chi_{570}(41, \cdot)$$ n/a 480 6
570.4.bc $$\chi_{570}(139, \cdot)$$ n/a 360 6
570.4.bf $$\chi_{570}(29, \cdot)$$ n/a 720 6
570.4.bh $$\chi_{570}(13, \cdot)$$ n/a 720 12
570.4.bi $$\chi_{570}(17, \cdot)$$ n/a 1440 12

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(570))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(570)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 2}$$