## Defining parameters

 Level: $$N$$ = $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$24$$ Sturm bound: $$184320$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(930))$$.

Total New Old
Modular forms 70080 15808 54272
Cusp forms 68160 15808 52352
Eisenstein series 1920 0 1920

## Trace form

 $$15808q - 28q^{3} - 8q^{5} + 8q^{6} - 80q^{7} + O(q^{10})$$ $$15808q - 28q^{3} - 8q^{5} + 8q^{6} - 80q^{7} + 80q^{10} - 64q^{11} + 16q^{12} + 304q^{13} + 128q^{14} + 476q^{15} + 256q^{16} + 144q^{17} + 32q^{18} - 32q^{19} + 32q^{20} + 80q^{21} + 4368q^{22} + 2976q^{23} - 96q^{24} - 640q^{25} - 1776q^{26} + 1268q^{27} - 4160q^{28} - 6288q^{29} - 1968q^{30} - 7152q^{31} - 3808q^{33} - 3872q^{34} - 1648q^{35} - 1024q^{36} + 3184q^{37} + 2256q^{38} + 5424q^{39} + 192q^{40} + 10352q^{41} + 8296q^{42} + 10336q^{43} + 1984q^{44} + 2728q^{45} + 2816q^{46} + 288q^{47} + 64q^{48} + 9336q^{49} + 352q^{50} + 8476q^{51} - 704q^{52} + 1032q^{53} - 216q^{54} - 5864q^{55} + 640q^{56} - 9700q^{57} - 5376q^{58} - 9880q^{59} - 2320q^{60} - 23080q^{61} - 1008q^{62} - 17200q^{63} - 10836q^{65} - 352q^{66} - 3032q^{67} + 576q^{68} - 132q^{69} + 5760q^{70} + 10416q^{71} - 128q^{72} + 7624q^{73} - 160q^{74} + 6922q^{75} + 1408q^{76} + 24936q^{77} - 13512q^{78} + 4144q^{79} - 128q^{80} - 1616q^{81} - 2688q^{82} + 2304q^{83} + 1824q^{84} + 1216q^{85} - 2912q^{86} + 6344q^{87} - 2688q^{88} - 2816q^{89} + 4712q^{90} - 5536q^{91} - 576q^{92} + 43456q^{93} - 4864q^{94} + 2352q^{95} + 640q^{96} + 17872q^{97} + 4032q^{98} + 19464q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(930))$$

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
930.4.a $$\chi_{930}(1, \cdot)$$ 930.4.a.a 1 1
930.4.a.b 1
930.4.a.c 1
930.4.a.d 2
930.4.a.e 2
930.4.a.f 3
930.4.a.g 3
930.4.a.h 3
930.4.a.i 3
930.4.a.j 4
930.4.a.k 4
930.4.a.l 4
930.4.a.m 4
930.4.a.n 4
930.4.a.o 5
930.4.a.p 5
930.4.a.q 5
930.4.a.r 6
930.4.d $$\chi_{930}(559, \cdot)$$ 930.4.d.a 2 1
930.4.d.b 20
930.4.d.c 20
930.4.d.d 24
930.4.d.e 26
930.4.e $$\chi_{930}(929, \cdot)$$ n/a 192 1
930.4.h $$\chi_{930}(371, \cdot)$$ n/a 128 1
930.4.i $$\chi_{930}(211, \cdot)$$ n/a 128 2
930.4.j $$\chi_{930}(497, \cdot)$$ n/a 360 2
930.4.k $$\chi_{930}(247, \cdot)$$ n/a 192 2
930.4.n $$\chi_{930}(481, \cdot)$$ n/a 256 4
930.4.o $$\chi_{930}(161, \cdot)$$ n/a 256 2
930.4.r $$\chi_{930}(119, \cdot)$$ n/a 384 2
930.4.s $$\chi_{930}(439, \cdot)$$ n/a 192 2
930.4.v $$\chi_{930}(401, \cdot)$$ n/a 512 4
930.4.y $$\chi_{930}(29, \cdot)$$ n/a 768 4
930.4.z $$\chi_{930}(109, \cdot)$$ n/a 384 4
930.4.be $$\chi_{930}(37, \cdot)$$ n/a 384 4
930.4.bf $$\chi_{930}(377, \cdot)$$ n/a 768 4
930.4.bg $$\chi_{930}(121, \cdot)$$ n/a 512 8
930.4.bj $$\chi_{930}(277, \cdot)$$ n/a 768 8
930.4.bk $$\chi_{930}(47, \cdot)$$ n/a 1536 8
930.4.bn $$\chi_{930}(19, \cdot)$$ n/a 768 8
930.4.bo $$\chi_{930}(179, \cdot)$$ n/a 1536 8
930.4.br $$\chi_{930}(11, \cdot)$$ n/a 1024 8
930.4.bs $$\chi_{930}(107, \cdot)$$ n/a 3072 16
930.4.bt $$\chi_{930}(13, \cdot)$$ n/a 1536 16

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(930))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(930)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(62))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(93))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(155))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(186))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(310))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(465))$$$$^{\oplus 2}$$