Properties

 Label 175.1 Level 175 Weight 1 Dimension 4 Nonzero newspaces 2 Newform subspaces 3 Sturm bound 2400 Trace bound 9

Defining parameters

 Level: $$N$$ = $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$3$$ Sturm bound: $$2400$$ Trace bound: $$9$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(175))$$.

Total New Old
Modular forms 172 107 65
Cusp forms 4 4 0
Eisenstein series 168 103 65

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

Trace form

 $$4 q + O(q^{10})$$ $$4 q - 4 q^{11} - 4 q^{16} + 4 q^{46} + 4 q^{56} - 4 q^{71} + 4 q^{81} + 4 q^{86} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(175))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
175.1.c $$\chi_{175}(174, \cdot)$$ 175.1.c.a 2 1
175.1.d $$\chi_{175}(76, \cdot)$$ 175.1.d.a 1 1
175.1.d.b 1
175.1.g $$\chi_{175}(43, \cdot)$$ None 0 2
175.1.i $$\chi_{175}(26, \cdot)$$ None 0 2
175.1.j $$\chi_{175}(24, \cdot)$$ None 0 2
175.1.l $$\chi_{175}(6, \cdot)$$ None 0 4
175.1.m $$\chi_{175}(34, \cdot)$$ None 0 4
175.1.p $$\chi_{175}(18, \cdot)$$ None 0 4
175.1.r $$\chi_{175}(8, \cdot)$$ None 0 8
175.1.u $$\chi_{175}(19, \cdot)$$ None 0 8
175.1.v $$\chi_{175}(31, \cdot)$$ None 0 8
175.1.w $$\chi_{175}(2, \cdot)$$ None 0 16