# Properties

 Label 1215.1 Level 1215 Weight 1 Dimension 18 Nonzero newspaces 2 Newform subspaces 4 Sturm bound 104976 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$1215 = 3^{5} \cdot 5$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$4$$ Sturm bound: $$104976$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1215))$$.

Total New Old
Modular forms 1550 594 956
Cusp forms 38 18 20
Eisenstein series 1512 576 936

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 18 0 0 0

## Trace form

 $$18 q + O(q^{10})$$ $$18 q - 18 q^{46} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1215))$$

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
1215.1.c $$\chi_{1215}(971, \cdot)$$ None 0 1
1215.1.d $$\chi_{1215}(1214, \cdot)$$ 1215.1.d.a 3 1
1215.1.d.b 3
1215.1.g $$\chi_{1215}(487, \cdot)$$ None 0 2
1215.1.h $$\chi_{1215}(404, \cdot)$$ 1215.1.h.a 6 2
1215.1.h.b 6
1215.1.i $$\chi_{1215}(161, \cdot)$$ None 0 2
1215.1.l $$\chi_{1215}(82, \cdot)$$ None 0 4
1215.1.n $$\chi_{1215}(134, \cdot)$$ None 0 6
1215.1.o $$\chi_{1215}(26, \cdot)$$ None 0 6
1215.1.s $$\chi_{1215}(28, \cdot)$$ None 0 12
1215.1.u $$\chi_{1215}(71, \cdot)$$ None 0 18
1215.1.v $$\chi_{1215}(44, \cdot)$$ None 0 18
1215.1.x $$\chi_{1215}(37, \cdot)$$ None 0 36
1215.1.z $$\chi_{1215}(11, \cdot)$$ None 0 54
1215.1.bb $$\chi_{1215}(14, \cdot)$$ None 0 54
1215.1.bc $$\chi_{1215}(7, \cdot)$$ None 0 108

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1215))$$ into lower level spaces

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