# Properties

 Label 105.2 Level 105 Weight 2 Dimension 227 Nonzero newspaces 12 Newforms 25 Sturm bound 1536 Trace bound 4

# Learn more about

## Defining parameters

 Level: $$N$$ = $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newforms: $$25$$ 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

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

## 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

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