# Properties

 Label 175.2 Level 175 Weight 2 Dimension 959 Nonzero newspaces 12 Newforms 32 Sturm bound 4800 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newforms: $$32$$ Sturm bound: $$4800$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(175))$$.

Total New Old
Modular forms 1368 1163 205
Cusp forms 1033 959 74
Eisenstein series 335 204 131

## Trace form

 $$959q$$ $$\mathstrut -\mathstrut 25q^{2}$$ $$\mathstrut -\mathstrut 28q^{3}$$ $$\mathstrut -\mathstrut 37q^{4}$$ $$\mathstrut -\mathstrut 38q^{5}$$ $$\mathstrut -\mathstrut 60q^{6}$$ $$\mathstrut -\mathstrut 41q^{7}$$ $$\mathstrut -\mathstrut 97q^{8}$$ $$\mathstrut -\mathstrut 55q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$959q$$ $$\mathstrut -\mathstrut 25q^{2}$$ $$\mathstrut -\mathstrut 28q^{3}$$ $$\mathstrut -\mathstrut 37q^{4}$$ $$\mathstrut -\mathstrut 38q^{5}$$ $$\mathstrut -\mathstrut 60q^{6}$$ $$\mathstrut -\mathstrut 41q^{7}$$ $$\mathstrut -\mathstrut 97q^{8}$$ $$\mathstrut -\mathstrut 55q^{9}$$ $$\mathstrut -\mathstrut 58q^{10}$$ $$\mathstrut -\mathstrut 60q^{11}$$ $$\mathstrut -\mathstrut 100q^{12}$$ $$\mathstrut -\mathstrut 58q^{13}$$ $$\mathstrut -\mathstrut 71q^{14}$$ $$\mathstrut -\mathstrut 116q^{15}$$ $$\mathstrut -\mathstrut 85q^{16}$$ $$\mathstrut -\mathstrut 50q^{17}$$ $$\mathstrut -\mathstrut 83q^{18}$$ $$\mathstrut -\mathstrut 36q^{19}$$ $$\mathstrut -\mathstrut 28q^{20}$$ $$\mathstrut -\mathstrut 82q^{21}$$ $$\mathstrut -\mathstrut 80q^{22}$$ $$\mathstrut -\mathstrut 48q^{23}$$ $$\mathstrut +\mathstrut 40q^{24}$$ $$\mathstrut -\mathstrut 6q^{25}$$ $$\mathstrut -\mathstrut 102q^{26}$$ $$\mathstrut -\mathstrut 4q^{27}$$ $$\mathstrut +\mathstrut 25q^{28}$$ $$\mathstrut -\mathstrut 54q^{29}$$ $$\mathstrut +\mathstrut 4q^{30}$$ $$\mathstrut -\mathstrut 32q^{31}$$ $$\mathstrut +\mathstrut 9q^{32}$$ $$\mathstrut -\mathstrut 8q^{34}$$ $$\mathstrut -\mathstrut 32q^{35}$$ $$\mathstrut -\mathstrut 53q^{36}$$ $$\mathstrut -\mathstrut 48q^{37}$$ $$\mathstrut -\mathstrut 40q^{38}$$ $$\mathstrut +\mathstrut 16q^{39}$$ $$\mathstrut -\mathstrut 6q^{40}$$ $$\mathstrut -\mathstrut 62q^{41}$$ $$\mathstrut +\mathstrut 38q^{42}$$ $$\mathstrut -\mathstrut 56q^{43}$$ $$\mathstrut -\mathstrut 32q^{44}$$ $$\mathstrut +\mathstrut 38q^{45}$$ $$\mathstrut -\mathstrut 72q^{46}$$ $$\mathstrut -\mathstrut 56q^{47}$$ $$\mathstrut +\mathstrut 56q^{48}$$ $$\mathstrut -\mathstrut 105q^{49}$$ $$\mathstrut -\mathstrut 46q^{50}$$ $$\mathstrut -\mathstrut 160q^{51}$$ $$\mathstrut +\mathstrut 6q^{52}$$ $$\mathstrut -\mathstrut 88q^{53}$$ $$\mathstrut +\mathstrut 28q^{54}$$ $$\mathstrut -\mathstrut 44q^{55}$$ $$\mathstrut -\mathstrut 79q^{56}$$ $$\mathstrut -\mathstrut 36q^{57}$$ $$\mathstrut +\mathstrut 46q^{58}$$ $$\mathstrut +\mathstrut 92q^{60}$$ $$\mathstrut +\mathstrut 14q^{61}$$ $$\mathstrut +\mathstrut 132q^{62}$$ $$\mathstrut +\mathstrut 61q^{63}$$ $$\mathstrut +\mathstrut 75q^{64}$$ $$\mathstrut +\mathstrut 14q^{65}$$ $$\mathstrut +\mathstrut 48q^{66}$$ $$\mathstrut +\mathstrut 52q^{67}$$ $$\mathstrut +\mathstrut 158q^{68}$$ $$\mathstrut +\mathstrut 52q^{69}$$ $$\mathstrut +\mathstrut 102q^{70}$$ $$\mathstrut -\mathstrut 124q^{71}$$ $$\mathstrut +\mathstrut 147q^{72}$$ $$\mathstrut +\mathstrut 34q^{73}$$ $$\mathstrut +\mathstrut 126q^{74}$$ $$\mathstrut +\mathstrut 28q^{75}$$ $$\mathstrut +\mathstrut 28q^{76}$$ $$\mathstrut +\mathstrut 18q^{77}$$ $$\mathstrut -\mathstrut 8q^{78}$$ $$\mathstrut +\mathstrut 16q^{79}$$ $$\mathstrut +\mathstrut 98q^{80}$$ $$\mathstrut -\mathstrut 91q^{81}$$ $$\mathstrut +\mathstrut 86q^{82}$$ $$\mathstrut +\mathstrut 48q^{83}$$ $$\mathstrut +\mathstrut 90q^{84}$$ $$\mathstrut +\mathstrut 22q^{85}$$ $$\mathstrut -\mathstrut 36q^{86}$$ $$\mathstrut +\mathstrut 4q^{87}$$ $$\mathstrut +\mathstrut 180q^{88}$$ $$\mathstrut +\mathstrut 84q^{89}$$ $$\mathstrut +\mathstrut 170q^{90}$$ $$\mathstrut -\mathstrut 56q^{91}$$ $$\mathstrut +\mathstrut 12q^{92}$$ $$\mathstrut +\mathstrut 28q^{93}$$ $$\mathstrut +\mathstrut 64q^{94}$$ $$\mathstrut +\mathstrut 28q^{95}$$ $$\mathstrut -\mathstrut 4q^{96}$$ $$\mathstrut +\mathstrut 114q^{97}$$ $$\mathstrut +\mathstrut 125q^{98}$$ $$\mathstrut -\mathstrut 68q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$

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
175.2.a $$\chi_{175}(1, \cdot)$$ 175.2.a.a 1 1
175.2.a.b 1
175.2.a.c 1
175.2.a.d 2
175.2.a.e 2
175.2.a.f 2
175.2.b $$\chi_{175}(99, \cdot)$$ 175.2.b.a 2 1
175.2.b.b 4
175.2.b.c 4
175.2.e $$\chi_{175}(51, \cdot)$$ 175.2.e.a 2 2
175.2.e.b 2
175.2.e.c 4
175.2.e.d 6
175.2.e.e 6
175.2.f $$\chi_{175}(118, \cdot)$$ 175.2.f.a 4 2
175.2.f.b 4
175.2.f.c 4
175.2.f.d 8
175.2.h $$\chi_{175}(36, \cdot)$$ 175.2.h.a 4 4
175.2.h.b 28
175.2.h.c 32
175.2.k $$\chi_{175}(74, \cdot)$$ 175.2.k.a 8 2
175.2.k.b 12
175.2.n $$\chi_{175}(29, \cdot)$$ 175.2.n.a 56 4
175.2.o $$\chi_{175}(68, \cdot)$$ 175.2.o.a 4 4
175.2.o.b 4
175.2.o.c 8
175.2.o.d 24
175.2.q $$\chi_{175}(11, \cdot)$$ 175.2.q.a 144 8
175.2.s $$\chi_{175}(13, \cdot)$$ 175.2.s.a 144 8
175.2.t $$\chi_{175}(4, \cdot)$$ 175.2.t.a 144 8
175.2.x $$\chi_{175}(3, \cdot)$$ 175.2.x.a 288 16

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(175))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(175)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 2}$$