## Defining parameters

 Level: $$N$$ = $$1225 = 5^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$7$$ Sturm bound: $$117600$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1225))$$.

Total New Old
Modular forms 1714 1020 694
Cusp forms 34 26 8
Eisenstein series 1680 994 686

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 26 0 0 0

## Trace form

 $$26q + O(q^{10})$$ $$26q + 4q^{11} + 4q^{16} - 18q^{36} - 4q^{46} - 8q^{71} - 4q^{81} - 4q^{86} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1225))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1225.1.c $$\chi_{1225}(1224, \cdot)$$ None 0 1
1225.1.d $$\chi_{1225}(1126, \cdot)$$ None 0 1
1225.1.g $$\chi_{1225}(393, \cdot)$$ 1225.1.g.a 2 2
1225.1.g.b 4
1225.1.i $$\chi_{1225}(276, \cdot)$$ 1225.1.i.a 2 2
1225.1.i.b 2
1225.1.j $$\chi_{1225}(374, \cdot)$$ 1225.1.j.a 4 2
1225.1.m $$\chi_{1225}(146, \cdot)$$ None 0 4
1225.1.n $$\chi_{1225}(244, \cdot)$$ None 0 4
1225.1.q $$\chi_{1225}(18, \cdot)$$ 1225.1.q.a 4 4
1225.1.q.b 8
1225.1.r $$\chi_{1225}(76, \cdot)$$ None 0 6
1225.1.s $$\chi_{1225}(174, \cdot)$$ None 0 6
1225.1.v $$\chi_{1225}(148, \cdot)$$ None 0 8
1225.1.y $$\chi_{1225}(43, \cdot)$$ None 0 12
1225.1.bb $$\chi_{1225}(19, \cdot)$$ None 0 8
1225.1.bc $$\chi_{1225}(31, \cdot)$$ None 0 8
1225.1.bf $$\chi_{1225}(24, \cdot)$$ None 0 12
1225.1.bg $$\chi_{1225}(26, \cdot)$$ None 0 12
1225.1.bh $$\chi_{1225}(67, \cdot)$$ None 0 16
1225.1.bk $$\chi_{1225}(34, \cdot)$$ None 0 24
1225.1.bl $$\chi_{1225}(6, \cdot)$$ None 0 24
1225.1.bm $$\chi_{1225}(32, \cdot)$$ None 0 24
1225.1.bq $$\chi_{1225}(8, \cdot)$$ None 0 48
1225.1.br $$\chi_{1225}(61, \cdot)$$ None 0 48
1225.1.bs $$\chi_{1225}(54, \cdot)$$ None 0 48
1225.1.bv $$\chi_{1225}(2, \cdot)$$ None 0 96

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1225))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1225)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 2}$$