## Defining parameters

 Level: $$N$$ = $$946 = 2 \cdot 11 \cdot 43$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$70$$ Sturm bound: $$110880$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(946))$$.

Total New Old
Modular forms 28560 9079 19481
Cusp forms 26881 9079 17802
Eisenstein series 1679 0 1679

## Trace form

 $$9079q + 3q^{2} + 12q^{3} + 3q^{4} + 18q^{5} + 2q^{6} + 4q^{7} + 3q^{8} - q^{9} + O(q^{10})$$ $$9079q + 3q^{2} + 12q^{3} + 3q^{4} + 18q^{5} + 2q^{6} + 4q^{7} + 3q^{8} - q^{9} - 2q^{10} + 3q^{11} - 8q^{12} + 22q^{13} + 4q^{14} + 12q^{15} + 3q^{16} + 14q^{17} + 29q^{18} + 30q^{19} + 18q^{20} + 56q^{21} + 23q^{22} + 32q^{23} + 2q^{24} + 13q^{25} + 2q^{26} + 30q^{27} + 4q^{28} + 10q^{29} + 12q^{30} + 8q^{31} - 7q^{32} - 102q^{33} - 112q^{34} - 144q^{35} - 83q^{36} - 94q^{37} - 168q^{38} - 128q^{39} - 2q^{40} - 38q^{41} - 132q^{42} - 383q^{43} - 49q^{44} - 286q^{45} - 136q^{46} - 20q^{47} + 12q^{48} - 145q^{49} - 115q^{50} - 82q^{51} - 110q^{52} - 106q^{53} - 86q^{54} - 86q^{55} + 24q^{56} + 42q^{57} + 10q^{58} + 50q^{59} + 32q^{60} + 46q^{61} + 36q^{62} + 72q^{63} + 3q^{64} + 52q^{65} - 28q^{66} + 24q^{67} + 14q^{68} - 16q^{69} + 64q^{70} - 28q^{71} - q^{72} + 18q^{73} + 74q^{74} - 152q^{75} + 40q^{76} - 102q^{77} + 88q^{78} - 28q^{79} - 2q^{80} - 243q^{81} + 56q^{82} - 46q^{83} + 16q^{84} - 64q^{85} + 22q^{86} - 260q^{87} + 3q^{88} - 58q^{89} + 54q^{90} - 32q^{91} + 12q^{92} - 212q^{93} + 24q^{94} - 28q^{95} + 12q^{96} - 148q^{97} + 81q^{98} - 108q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(946))$$

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
946.2.a $$\chi_{946}(1, \cdot)$$ 946.2.a.a 1 1
946.2.a.b 1
946.2.a.c 1
946.2.a.d 2
946.2.a.e 2
946.2.a.f 2
946.2.a.g 4
946.2.a.h 4
946.2.a.i 5
946.2.a.j 6
946.2.a.k 7
946.2.c $$\chi_{946}(945, \cdot)$$ 946.2.c.a 22 1
946.2.c.b 22
946.2.e $$\chi_{946}(221, \cdot)$$ 946.2.e.a 2 2
946.2.e.b 2
946.2.e.c 2
946.2.e.d 2
946.2.e.e 2
946.2.e.f 2
946.2.e.g 2
946.2.e.h 2
946.2.e.i 2
946.2.e.j 4
946.2.e.k 8
946.2.e.l 12
946.2.e.m 16
946.2.e.n 18
946.2.f $$\chi_{946}(345, \cdot)$$ 946.2.f.a 4 4
946.2.f.b 4
946.2.f.c 8
946.2.f.d 16
946.2.f.e 24
946.2.f.f 32
946.2.f.g 40
946.2.f.h 40
946.2.h $$\chi_{946}(351, \cdot)$$ 946.2.h.a 4 2
946.2.h.b 4
946.2.h.c 4
946.2.h.d 4
946.2.h.e 36
946.2.h.f 36
946.2.j $$\chi_{946}(133, \cdot)$$ 946.2.j.a 6 6
946.2.j.b 6
946.2.j.c 36
946.2.j.d 48
946.2.j.e 54
946.2.j.f 54
946.2.l $$\chi_{946}(85, \cdot)$$ 946.2.l.a 88 4
946.2.l.b 88
946.2.p $$\chi_{946}(65, \cdot)$$ 946.2.p.a 132 6
946.2.p.b 132
946.2.q $$\chi_{946}(49, \cdot)$$ 946.2.q.a 8 8
946.2.q.b 168
946.2.q.c 176
946.2.r $$\chi_{946}(23, \cdot)$$ 946.2.r.a 108 12
946.2.r.b 108
946.2.r.c 120
946.2.r.d 120
946.2.t $$\chi_{946}(7, \cdot)$$ 946.2.t.a 176 8
946.2.t.b 176
946.2.v $$\chi_{946}(47, \cdot)$$ 946.2.v.a 504 24
946.2.v.b 552
946.2.w $$\chi_{946}(175, \cdot)$$ 946.2.w.a 264 12
946.2.w.b 264
946.2.z $$\chi_{946}(39, \cdot)$$ 946.2.z.a 528 24
946.2.z.b 528
946.2.bc $$\chi_{946}(9, \cdot)$$ 946.2.bc.a 1008 48
946.2.bc.b 1104
946.2.bf $$\chi_{946}(19, \cdot)$$ 946.2.bf.a 1056 48
946.2.bf.b 1056

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(946))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(946)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(43))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(86))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(473))$$$$^{\oplus 2}$$