## Defining parameters

 Level: $$N$$ = $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$25$$ Sturm bound: $$1536$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(105))$$.

Total New Old
Modular forms 480 283 197
Cusp forms 289 227 62
Eisenstein series 191 56 135

## Trace form

 $$227 q + 5 q^{2} - 5 q^{3} - 19 q^{4} - 7 q^{5} - 35 q^{6} - 21 q^{7} - 27 q^{8} - 21 q^{9} + O(q^{10})$$ $$227 q + 5 q^{2} - 5 q^{3} - 19 q^{4} - 7 q^{5} - 35 q^{6} - 21 q^{7} - 27 q^{8} - 21 q^{9} - 43 q^{10} - 16 q^{11} - 27 q^{12} - 34 q^{13} - 27 q^{14} - 21 q^{15} - 75 q^{16} - 10 q^{17} - 7 q^{18} - 40 q^{19} - 27 q^{20} - 25 q^{21} - 68 q^{22} - 24 q^{23} + 21 q^{24} - 37 q^{25} + 2 q^{26} + 19 q^{27} - 11 q^{28} + 10 q^{29} + 37 q^{30} - 44 q^{31} + 85 q^{32} + 16 q^{33} + 34 q^{34} + 37 q^{35} + 61 q^{36} + 26 q^{37} + 56 q^{38} + 30 q^{39} + 45 q^{40} + 22 q^{41} + 57 q^{42} - 44 q^{43} + 4 q^{44} + 17 q^{45} - 72 q^{46} - 52 q^{47} + 45 q^{48} - 57 q^{49} - 55 q^{50} - 26 q^{51} - 18 q^{52} - 22 q^{53} - 11 q^{54} - 28 q^{55} - 3 q^{56} - 36 q^{57} + 86 q^{58} - 4 q^{59} + 65 q^{60} + 38 q^{61} + 48 q^{62} - 25 q^{63} + 85 q^{64} + 72 q^{65} + 92 q^{66} + 80 q^{67} + 130 q^{68} + 72 q^{69} + 249 q^{70} + 64 q^{71} + 57 q^{72} + 134 q^{73} + 154 q^{74} + 91 q^{75} + 108 q^{76} + 84 q^{77} + 70 q^{78} + 92 q^{79} + 69 q^{80} - 9 q^{81} + 74 q^{82} - 12 q^{83} - 31 q^{84} - 58 q^{85} - 16 q^{86} - 46 q^{87} - 12 q^{88} - 18 q^{89} - 115 q^{90} - 158 q^{91} - 168 q^{92} - 80 q^{93} - 176 q^{94} - 102 q^{95} - 271 q^{96} - 138 q^{97} - 167 q^{98} - 124 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$

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
105.2.a $$\chi_{105}(1, \cdot)$$ 105.2.a.a 1 1
105.2.a.b 2
105.2.b $$\chi_{105}(41, \cdot)$$ 105.2.b.a 2 1
105.2.b.b 2
105.2.b.c 4
105.2.b.d 4
105.2.d $$\chi_{105}(64, \cdot)$$ 105.2.d.a 2 1
105.2.d.b 6
105.2.g $$\chi_{105}(104, \cdot)$$ 105.2.g.a 4 1
105.2.g.b 4
105.2.g.c 4
105.2.i $$\chi_{105}(16, \cdot)$$ 105.2.i.a 2 2
105.2.i.b 2
105.2.i.c 4
105.2.i.d 4
105.2.j $$\chi_{105}(8, \cdot)$$ 105.2.j.a 24 2
105.2.m $$\chi_{105}(13, \cdot)$$ 105.2.m.a 16 2
105.2.p $$\chi_{105}(59, \cdot)$$ 105.2.p.a 24 2
105.2.q $$\chi_{105}(4, \cdot)$$ 105.2.q.a 16 2
105.2.s $$\chi_{105}(26, \cdot)$$ 105.2.s.a 2 2
105.2.s.b 2
105.2.s.c 8
105.2.s.d 8
105.2.u $$\chi_{105}(52, \cdot)$$ 105.2.u.a 32 4
105.2.x $$\chi_{105}(2, \cdot)$$ 105.2.x.a 48 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(105))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(105)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 2}$$