## 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

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

## 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

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