# Properties

 Label 3645.1 Level 3645 Weight 1 Dimension 48 Nonzero newspaces 1 Newform subspaces 8 Sturm bound 944784 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$3645 = 3^{6} \cdot 5$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$8$$ Sturm bound: $$944784$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(3645))$$.

Total New Old
Modular forms 5312 1992 3320
Cusp forms 128 48 80
Eisenstein series 5184 1944 3240

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 48 0 0 0

## Trace form

 $$48 q + O(q^{10})$$ $$48 q + 6 q^{10} + 6 q^{19} + 12 q^{46} - 6 q^{64} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(3645))$$

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
3645.1.c $$\chi_{3645}(2186, \cdot)$$ None 0 1
3645.1.d $$\chi_{3645}(3644, \cdot)$$ None 0 1
3645.1.g $$\chi_{3645}(2188, \cdot)$$ None 0 2
3645.1.h $$\chi_{3645}(1214, \cdot)$$ None 0 2
3645.1.i $$\chi_{3645}(971, \cdot)$$ None 0 2
3645.1.l $$\chi_{3645}(487, \cdot)$$ None 0 4
3645.1.n $$\chi_{3645}(404, \cdot)$$ 3645.1.n.a 6 6
3645.1.n.b 6
3645.1.n.c 6
3645.1.n.d 6
3645.1.n.e 6
3645.1.n.f 6
3645.1.n.g 6
3645.1.n.h 6
3645.1.o $$\chi_{3645}(161, \cdot)$$ None 0 6
3645.1.s $$\chi_{3645}(82, \cdot)$$ None 0 12
3645.1.u $$\chi_{3645}(26, \cdot)$$ None 0 18
3645.1.v $$\chi_{3645}(134, \cdot)$$ None 0 18
3645.1.x $$\chi_{3645}(28, \cdot)$$ None 0 36
3645.1.z $$\chi_{3645}(71, \cdot)$$ None 0 54
3645.1.bb $$\chi_{3645}(44, \cdot)$$ None 0 54
3645.1.bd $$\chi_{3645}(37, \cdot)$$ None 0 108
3645.1.bf $$\chi_{3645}(14, \cdot)$$ None 0 162
3645.1.bg $$\chi_{3645}(11, \cdot)$$ None 0 162
3645.1.bi $$\chi_{3645}(7, \cdot)$$ None 0 324

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(3645))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(3645)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(243))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(405))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(729))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1215))$$$$^{\oplus 2}$$