# Properties

 Label 170.2 Level 170 Weight 2 Dimension 265 Nonzero newspaces 10 Newforms 30 Sturm bound 3456 Trace bound 10

## Defining parameters

 Level: $$N$$ = $$170 = 2 \cdot 5 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$10$$ Newforms: $$30$$ Sturm bound: $$3456$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(170))$$.

Total New Old
Modular forms 992 265 727
Cusp forms 737 265 472
Eisenstein series 255 0 255

## Trace form

 $$265q$$ $$\mathstrut +\mathstrut q^{2}$$ $$\mathstrut +\mathstrut 4q^{3}$$ $$\mathstrut +\mathstrut q^{4}$$ $$\mathstrut +\mathstrut q^{5}$$ $$\mathstrut +\mathstrut 4q^{6}$$ $$\mathstrut +\mathstrut 8q^{7}$$ $$\mathstrut +\mathstrut q^{8}$$ $$\mathstrut +\mathstrut 13q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$265q$$ $$\mathstrut +\mathstrut q^{2}$$ $$\mathstrut +\mathstrut 4q^{3}$$ $$\mathstrut +\mathstrut q^{4}$$ $$\mathstrut +\mathstrut q^{5}$$ $$\mathstrut +\mathstrut 4q^{6}$$ $$\mathstrut +\mathstrut 8q^{7}$$ $$\mathstrut +\mathstrut q^{8}$$ $$\mathstrut +\mathstrut 13q^{9}$$ $$\mathstrut -\mathstrut 3q^{10}$$ $$\mathstrut -\mathstrut 20q^{11}$$ $$\mathstrut -\mathstrut 12q^{12}$$ $$\mathstrut -\mathstrut 18q^{13}$$ $$\mathstrut -\mathstrut 24q^{14}$$ $$\mathstrut -\mathstrut 44q^{15}$$ $$\mathstrut -\mathstrut 7q^{16}$$ $$\mathstrut -\mathstrut 15q^{17}$$ $$\mathstrut -\mathstrut 51q^{18}$$ $$\mathstrut -\mathstrut 12q^{19}$$ $$\mathstrut -\mathstrut 3q^{20}$$ $$\mathstrut -\mathstrut 64q^{21}$$ $$\mathstrut -\mathstrut 20q^{22}$$ $$\mathstrut -\mathstrut 8q^{23}$$ $$\mathstrut -\mathstrut 12q^{24}$$ $$\mathstrut -\mathstrut 35q^{25}$$ $$\mathstrut +\mathstrut 6q^{26}$$ $$\mathstrut -\mathstrut 8q^{27}$$ $$\mathstrut +\mathstrut 8q^{28}$$ $$\mathstrut -\mathstrut 10q^{29}$$ $$\mathstrut +\mathstrut 4q^{30}$$ $$\mathstrut -\mathstrut 32q^{31}$$ $$\mathstrut +\mathstrut q^{32}$$ $$\mathstrut -\mathstrut 16q^{33}$$ $$\mathstrut +\mathstrut 17q^{34}$$ $$\mathstrut -\mathstrut 24q^{35}$$ $$\mathstrut +\mathstrut 13q^{36}$$ $$\mathstrut -\mathstrut 26q^{37}$$ $$\mathstrut +\mathstrut 4q^{38}$$ $$\mathstrut -\mathstrut 72q^{39}$$ $$\mathstrut +\mathstrut q^{40}$$ $$\mathstrut -\mathstrut 94q^{41}$$ $$\mathstrut -\mathstrut 64q^{42}$$ $$\mathstrut -\mathstrut 68q^{43}$$ $$\mathstrut -\mathstrut 52q^{44}$$ $$\mathstrut -\mathstrut 71q^{45}$$ $$\mathstrut -\mathstrut 40q^{46}$$ $$\mathstrut -\mathstrut 112q^{47}$$ $$\mathstrut +\mathstrut 4q^{48}$$ $$\mathstrut -\mathstrut 71q^{49}$$ $$\mathstrut -\mathstrut 15q^{50}$$ $$\mathstrut -\mathstrut 60q^{51}$$ $$\mathstrut -\mathstrut 50q^{52}$$ $$\mathstrut -\mathstrut 82q^{53}$$ $$\mathstrut -\mathstrut 72q^{54}$$ $$\mathstrut -\mathstrut 68q^{55}$$ $$\mathstrut +\mathstrut 8q^{56}$$ $$\mathstrut -\mathstrut 96q^{57}$$ $$\mathstrut -\mathstrut 34q^{58}$$ $$\mathstrut -\mathstrut 100q^{59}$$ $$\mathstrut -\mathstrut 28q^{60}$$ $$\mathstrut -\mathstrut 34q^{61}$$ $$\mathstrut -\mathstrut 64q^{62}$$ $$\mathstrut -\mathstrut 88q^{63}$$ $$\mathstrut +\mathstrut q^{64}$$ $$\mathstrut -\mathstrut 22q^{65}$$ $$\mathstrut +\mathstrut 32q^{66}$$ $$\mathstrut +\mathstrut 36q^{67}$$ $$\mathstrut +\mathstrut 25q^{68}$$ $$\mathstrut +\mathstrut 96q^{69}$$ $$\mathstrut +\mathstrut 104q^{70}$$ $$\mathstrut +\mathstrut 104q^{71}$$ $$\mathstrut +\mathstrut 53q^{72}$$ $$\mathstrut +\mathstrut 226q^{73}$$ $$\mathstrut +\mathstrut 110q^{74}$$ $$\mathstrut +\mathstrut 148q^{75}$$ $$\mathstrut +\mathstrut 20q^{76}$$ $$\mathstrut +\mathstrut 192q^{77}$$ $$\mathstrut +\mathstrut 184q^{78}$$ $$\mathstrut +\mathstrut 176q^{79}$$ $$\mathstrut +\mathstrut 49q^{80}$$ $$\mathstrut +\mathstrut 297q^{81}$$ $$\mathstrut +\mathstrut 178q^{82}$$ $$\mathstrut +\mathstrut 132q^{83}$$ $$\mathstrut +\mathstrut 96q^{84}$$ $$\mathstrut +\mathstrut 269q^{85}$$ $$\mathstrut +\mathstrut 108q^{86}$$ $$\mathstrut +\mathstrut 216q^{87}$$ $$\mathstrut +\mathstrut 76q^{88}$$ $$\mathstrut +\mathstrut 90q^{89}$$ $$\mathstrut +\mathstrut 217q^{90}$$ $$\mathstrut +\mathstrut 176q^{91}$$ $$\mathstrut +\mathstrut 56q^{92}$$ $$\mathstrut +\mathstrut 128q^{93}$$ $$\mathstrut +\mathstrut 176q^{94}$$ $$\mathstrut +\mathstrut 132q^{95}$$ $$\mathstrut +\mathstrut 4q^{96}$$ $$\mathstrut +\mathstrut 162q^{97}$$ $$\mathstrut +\mathstrut 129q^{98}$$ $$\mathstrut +\mathstrut 108q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(170))$$

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
170.2.a $$\chi_{170}(1, \cdot)$$ 170.2.a.a 1 1
170.2.a.b 1
170.2.a.c 1
170.2.a.d 1
170.2.a.e 1
170.2.a.f 2
170.2.b $$\chi_{170}(101, \cdot)$$ 170.2.b.a 2 1
170.2.b.b 2
170.2.b.c 2
170.2.c $$\chi_{170}(69, \cdot)$$ 170.2.c.a 2 1
170.2.c.b 6
170.2.d $$\chi_{170}(169, \cdot)$$ 170.2.d.a 2 1
170.2.d.b 2
170.2.d.c 4
170.2.g $$\chi_{170}(89, \cdot)$$ 170.2.g.a 2 2
170.2.g.b 2
170.2.g.c 2
170.2.g.d 2
170.2.g.e 4
170.2.g.f 4
170.2.h $$\chi_{170}(21, \cdot)$$ 170.2.h.a 4 2
170.2.h.b 8
170.2.k $$\chi_{170}(111, \cdot)$$ 170.2.k.a 8 4
170.2.k.b 16
170.2.n $$\chi_{170}(9, \cdot)$$ 170.2.n.a 20 4
170.2.n.b 20
170.2.o $$\chi_{170}(3, \cdot)$$ 170.2.o.a 32 8
170.2.o.b 40
170.2.r $$\chi_{170}(23, \cdot)$$ 170.2.r.a 32 8
170.2.r.b 40

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(170))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(170)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(85))$$$$^{\oplus 2}$$