## Defining parameters

 Level: $$N$$ = $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Newform subspaces: $$108$$ Sturm bound: $$92160$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(930))$$.

Total New Old
Modular forms 24000 5265 18735
Cusp forms 22081 5265 16816
Eisenstein series 1919 0 1919

## Trace form

 $$5265q + q^{2} + 5q^{3} + q^{4} + 9q^{5} + 5q^{6} + 8q^{7} + q^{8} + q^{9} + O(q^{10})$$ $$5265q + q^{2} + 5q^{3} + q^{4} + 9q^{5} + 5q^{6} + 8q^{7} + q^{8} + q^{9} - 7q^{10} - 20q^{11} - 11q^{12} - 18q^{13} - 24q^{14} - 19q^{15} + q^{16} - 30q^{17} - 15q^{18} - 12q^{19} - 7q^{20} + 12q^{21} + 116q^{22} + 96q^{23} + 5q^{24} + 57q^{25} + 134q^{26} + 5q^{27} + 168q^{28} + 222q^{29} + 89q^{30} + 225q^{31} + q^{32} + 116q^{33} + 226q^{34} + 96q^{35} + 21q^{36} + 270q^{37} + 92q^{38} + 98q^{39} - 23q^{40} + 82q^{41} + 36q^{42} - 44q^{43} - 4q^{44} + 9q^{45} - 72q^{46} - 48q^{47} - 11q^{48} + 33q^{49} - 15q^{50} + 174q^{51} - 18q^{52} + 78q^{53} + 5q^{54} + 100q^{55} - 8q^{56} + 200q^{57} - 2q^{58} + 100q^{59} + 13q^{60} + 358q^{61} - 23q^{62} + 248q^{63} + q^{64} + 194q^{65} - 36q^{66} + 92q^{67} - 30q^{68} + 172q^{69} + 8q^{70} + 120q^{71} + 17q^{72} + 82q^{73} - 42q^{74} + 17q^{75} - 44q^{76} + 24q^{77} - 190q^{78} - 96q^{79} + 9q^{80} - 303q^{81} - 22q^{82} - 108q^{83} - 128q^{84} - 30q^{85} - 68q^{86} - 298q^{87} - 4q^{88} - 166q^{89} - 203q^{90} - 144q^{91} - 24q^{92} - 527q^{93} - 16q^{94} - 28q^{95} - 11q^{96} - 126q^{97} - 39q^{98} - 304q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(930))$$

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
930.2.a $$\chi_{930}(1, \cdot)$$ 930.2.a.a 1 1
930.2.a.b 1
930.2.a.c 1
930.2.a.d 1
930.2.a.e 1
930.2.a.f 1
930.2.a.g 1
930.2.a.h 1
930.2.a.i 1
930.2.a.j 1
930.2.a.k 1
930.2.a.l 1
930.2.a.m 1
930.2.a.n 1
930.2.a.o 1
930.2.a.p 2
930.2.a.q 2
930.2.a.r 2
930.2.d $$\chi_{930}(559, \cdot)$$ 930.2.d.a 2 1
930.2.d.b 2
930.2.d.c 2
930.2.d.d 2
930.2.d.e 2
930.2.d.f 2
930.2.d.g 4
930.2.d.h 6
930.2.d.i 6
930.2.e $$\chi_{930}(929, \cdot)$$ 930.2.e.a 32 1
930.2.e.b 32
930.2.h $$\chi_{930}(371, \cdot)$$ 930.2.h.a 4 1
930.2.h.b 4
930.2.h.c 16
930.2.h.d 16
930.2.i $$\chi_{930}(211, \cdot)$$ 930.2.i.a 2 2
930.2.i.b 2
930.2.i.c 2
930.2.i.d 2
930.2.i.e 2
930.2.i.f 2
930.2.i.g 2
930.2.i.h 2
930.2.i.i 2
930.2.i.j 4
930.2.i.k 4
930.2.i.l 4
930.2.i.m 4
930.2.i.n 6
930.2.j $$\chi_{930}(497, \cdot)$$ 930.2.j.a 4 2
930.2.j.b 4
930.2.j.c 8
930.2.j.d 8
930.2.j.e 8
930.2.j.f 8
930.2.j.g 40
930.2.j.h 40
930.2.k $$\chi_{930}(247, \cdot)$$ 930.2.k.a 32 2
930.2.k.b 32
930.2.n $$\chi_{930}(481, \cdot)$$ 930.2.n.a 8 4
930.2.n.b 8
930.2.n.c 12
930.2.n.d 12
930.2.n.e 12
930.2.n.f 12
930.2.n.g 16
930.2.n.h 16
930.2.o $$\chi_{930}(161, \cdot)$$ 930.2.o.a 4 2
930.2.o.b 4
930.2.o.c 4
930.2.o.d 36
930.2.o.e 40
930.2.r $$\chi_{930}(119, \cdot)$$ 930.2.r.a 64 2
930.2.r.b 64
930.2.s $$\chi_{930}(439, \cdot)$$ 930.2.s.a 4 2
930.2.s.b 8
930.2.s.c 24
930.2.s.d 28
930.2.v $$\chi_{930}(401, \cdot)$$ 930.2.v.a 80 4
930.2.v.b 80
930.2.y $$\chi_{930}(29, \cdot)$$ 930.2.y.a 128 4
930.2.y.b 128
930.2.z $$\chi_{930}(109, \cdot)$$ 930.2.z.a 8 4
930.2.z.b 16
930.2.z.c 32
930.2.z.d 72
930.2.be $$\chi_{930}(37, \cdot)$$ 930.2.be.a 64 4
930.2.be.b 64
930.2.bf $$\chi_{930}(377, \cdot)$$ 930.2.bf.a 256 4
930.2.bg $$\chi_{930}(121, \cdot)$$ 930.2.bg.a 8 8
930.2.bg.b 16
930.2.bg.c 16
930.2.bg.d 16
930.2.bg.e 16
930.2.bg.f 16
930.2.bg.g 24
930.2.bg.h 24
930.2.bg.i 24
930.2.bj $$\chi_{930}(277, \cdot)$$ 930.2.bj.a 128 8
930.2.bj.b 128
930.2.bk $$\chi_{930}(47, \cdot)$$ 930.2.bk.a 512 8
930.2.bn $$\chi_{930}(19, \cdot)$$ 930.2.bn.a 112 8
930.2.bn.b 144
930.2.bo $$\chi_{930}(179, \cdot)$$ 930.2.bo.a 256 8
930.2.bo.b 256
930.2.br $$\chi_{930}(11, \cdot)$$ 930.2.br.a 176 8
930.2.br.b 176
930.2.bs $$\chi_{930}(107, \cdot)$$ 930.2.bs.a 1024 16
930.2.bt $$\chi_{930}(13, \cdot)$$ 930.2.bt.a 256 16
930.2.bt.b 256

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(930))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(930)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(62))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(93))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(155))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(186))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(310))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(465))$$$$^{\oplus 2}$$