# Properties

 Label 2025.1 Level 2025 Weight 1 Dimension 48 Nonzero newspaces 4 Newform subspaces 8 Sturm bound 291600 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$2025 = 3^{4} \cdot 5^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$8$$ Sturm bound: $$291600$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2025))$$.

Total New Old
Modular forms 3138 1196 1942
Cusp forms 114 48 66
Eisenstein series 3024 1148 1876

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 32 0 0 16

## Trace form

 $$48 q + 4 q^{4} + 4 q^{7} + O(q^{10})$$ $$48 q + 4 q^{4} + 4 q^{7} - 8 q^{10} + 8 q^{16} + 8 q^{19} + 4 q^{22} - 2 q^{25} + 4 q^{28} + 2 q^{31} - 4 q^{34} + 8 q^{37} + 2 q^{40} - 28 q^{46} - 2 q^{49} - 16 q^{55} + 2 q^{58} + 8 q^{61} - 16 q^{64} + 4 q^{67} - 12 q^{70} - 8 q^{76} + 4 q^{79} + 8 q^{82} - 2 q^{85} + 2 q^{88} - 16 q^{91} - 6 q^{94} + 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2025))$$

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
2025.1.c $$\chi_{2025}(1376, \cdot)$$ None 0 1
2025.1.d $$\chi_{2025}(2024, \cdot)$$ None 0 1
2025.1.g $$\chi_{2025}(82, \cdot)$$ None 0 2
2025.1.i $$\chi_{2025}(674, \cdot)$$ 2025.1.i.a 4 2
2025.1.j $$\chi_{2025}(26, \cdot)$$ 2025.1.j.a 2 2
2025.1.j.b 2
2025.1.j.c 4
2025.1.m $$\chi_{2025}(404, \cdot)$$ None 0 4
2025.1.o $$\chi_{2025}(161, \cdot)$$ None 0 4
2025.1.p $$\chi_{2025}(757, \cdot)$$ 2025.1.p.a 4 4
2025.1.p.b 8
2025.1.p.c 8
2025.1.s $$\chi_{2025}(224, \cdot)$$ None 0 6
2025.1.t $$\chi_{2025}(251, \cdot)$$ None 0 6
2025.1.v $$\chi_{2025}(163, \cdot)$$ None 0 8
2025.1.y $$\chi_{2025}(296, \cdot)$$ 2025.1.y.a 16 8
2025.1.ba $$\chi_{2025}(134, \cdot)$$ None 0 8
2025.1.bc $$\chi_{2025}(118, \cdot)$$ None 0 12
2025.1.bf $$\chi_{2025}(101, \cdot)$$ None 0 18
2025.1.bg $$\chi_{2025}(74, \cdot)$$ None 0 18
2025.1.bi $$\chi_{2025}(28, \cdot)$$ None 0 16
2025.1.bj $$\chi_{2025}(71, \cdot)$$ None 0 24
2025.1.bl $$\chi_{2025}(44, \cdot)$$ None 0 24
2025.1.bm $$\chi_{2025}(7, \cdot)$$ None 0 36
2025.1.bq $$\chi_{2025}(37, \cdot)$$ None 0 48
2025.1.bs $$\chi_{2025}(14, \cdot)$$ None 0 72
2025.1.bt $$\chi_{2025}(11, \cdot)$$ None 0 72
2025.1.bu $$\chi_{2025}(13, \cdot)$$ None 0 144

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(2025))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(2025)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(405))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(675))$$$$^{\oplus 2}$$