# Properties

 Label 3525.1 Level 3525 Weight 1 Dimension 192 Nonzero newspaces 3 Newform subspaces 6 Sturm bound 883200 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$3525 = 3 \cdot 5^{2} \cdot 47$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$6$$ Sturm bound: $$883200$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(3525))$$.

Total New Old
Modular forms 5496 2036 3460
Cusp forms 344 192 152
Eisenstein series 5152 1844 3308

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 192 0 0 0

## Trace form

 $$192 q + 6 q^{4} - 12 q^{6} + 2 q^{9} + O(q^{10})$$ $$192 q + 6 q^{4} - 12 q^{6} + 2 q^{9} - 50 q^{16} + 4 q^{19} + 8 q^{24} - 4 q^{31} + 8 q^{34} - 18 q^{36} - 8 q^{46} + 2 q^{49} - 12 q^{51} + 4 q^{54} + 4 q^{61} + 14 q^{64} + 4 q^{69} - 58 q^{76} + 4 q^{79} + 2 q^{81} - 42 q^{94} - 34 q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(3525))$$

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
3525.1.b $$\chi_{3525}(1174, \cdot)$$ None 0 1
3525.1.d $$\chi_{3525}(2351, \cdot)$$ None 0 1
3525.1.f $$\chi_{3525}(2774, \cdot)$$ None 0 1
3525.1.h $$\chi_{3525}(751, \cdot)$$ None 0 1
3525.1.k $$\chi_{3525}(1693, \cdot)$$ None 0 2
3525.1.l $$\chi_{3525}(1268, \cdot)$$ 3525.1.l.a 4 2
3525.1.l.b 8
3525.1.l.c 16
3525.1.l.d 32
3525.1.o $$\chi_{3525}(659, \cdot)$$ None 0 4
3525.1.p $$\chi_{3525}(46, \cdot)$$ None 0 4
3525.1.r $$\chi_{3525}(469, \cdot)$$ None 0 4
3525.1.t $$\chi_{3525}(236, \cdot)$$ None 0 4
3525.1.u $$\chi_{3525}(422, \cdot)$$ None 0 8
3525.1.v $$\chi_{3525}(142, \cdot)$$ None 0 8
3525.1.z $$\chi_{3525}(76, \cdot)$$ None 0 22
3525.1.bb $$\chi_{3525}(74, \cdot)$$ None 0 22
3525.1.bd $$\chi_{3525}(101, \cdot)$$ 3525.1.bd.a 44 22
3525.1.bf $$\chi_{3525}(124, \cdot)$$ None 0 22
3525.1.bg $$\chi_{3525}(107, \cdot)$$ 3525.1.bg.a 88 44
3525.1.bh $$\chi_{3525}(7, \cdot)$$ None 0 44
3525.1.bl $$\chi_{3525}(56, \cdot)$$ None 0 88
3525.1.bn $$\chi_{3525}(19, \cdot)$$ None 0 88
3525.1.bp $$\chi_{3525}(31, \cdot)$$ None 0 88
3525.1.bq $$\chi_{3525}(14, \cdot)$$ None 0 88
3525.1.bu $$\chi_{3525}(28, \cdot)$$ None 0 176
3525.1.bv $$\chi_{3525}(23, \cdot)$$ None 0 176

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(3525))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(3525)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(47))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(705))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1175))$$$$^{\oplus 2}$$