# Properties

 Label 93.1 Level 93 Weight 1 Dimension 4 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 640 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$93 = 3 \cdot 31$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$640$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(93))$$.

Total New Old
Modular forms 66 32 34
Cusp forms 6 4 2
Eisenstein series 60 28 32

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4 q - q^{3} - q^{4} - 2 q^{7} - q^{9} + O(q^{10})$$ $$4 q - q^{3} - q^{4} - 2 q^{7} - q^{9} - q^{12} - 2 q^{13} - q^{16} - 2 q^{19} + 3 q^{21} + 4 q^{25} - q^{27} + 3 q^{28} - q^{31} + 4 q^{36} - 2 q^{37} + 3 q^{39} + 3 q^{43} - q^{48} - 3 q^{49} - 2 q^{52} - 2 q^{57} - 2 q^{61} - 2 q^{63} - q^{64} - 2 q^{67} - 2 q^{73} - q^{75} + 3 q^{76} + 3 q^{79} - q^{81} - 2 q^{84} + q^{91} - q^{93} + 3 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(93))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
93.1.b $$\chi_{93}(32, \cdot)$$ None 0 1
93.1.d $$\chi_{93}(61, \cdot)$$ None 0 1
93.1.h $$\chi_{93}(5, \cdot)$$ None 0 2
93.1.i $$\chi_{93}(37, \cdot)$$ None 0 2
93.1.j $$\chi_{93}(46, \cdot)$$ None 0 4
93.1.l $$\chi_{93}(2, \cdot)$$ 93.1.l.a 4 4
93.1.n $$\chi_{93}(13, \cdot)$$ None 0 8
93.1.o $$\chi_{93}(14, \cdot)$$ None 0 8

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(93))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(93)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 2}$$