# Properties

 Label 363.1 Level 363 Weight 1 Dimension 5 Nonzero newspaces 2 Newform subspaces 2 Sturm bound 9680 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$363 = 3 \cdot 11^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$9680$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(363))$$.

Total New Old
Modular forms 325 146 179
Cusp forms 5 5 0
Eisenstein series 320 141 179

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 5 0 0 0

## Trace form

 $$5q + O(q^{10})$$ $$5q - 5q^{12} - 10q^{67} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(363))$$

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
363.1.b $$\chi_{363}(122, \cdot)$$ 363.1.b.a 1 1
363.1.c $$\chi_{363}(241, \cdot)$$ None 0 1
363.1.g $$\chi_{363}(40, \cdot)$$ None 0 4
363.1.h $$\chi_{363}(245, \cdot)$$ 363.1.h.a 4 4
363.1.k $$\chi_{363}(10, \cdot)$$ None 0 10
363.1.l $$\chi_{363}(23, \cdot)$$ None 0 10
363.1.n $$\chi_{363}(5, \cdot)$$ None 0 40
363.1.o $$\chi_{363}(7, \cdot)$$ None 0 40