## Defining parameters

 Level: $$N$$ = $$196 = 2^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$2352$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(196))$$.

Total New Old
Modular forms 153 52 101
Cusp forms 3 3 0
Eisenstein series 150 49 101

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 3 0 0 0

## Trace form

 $$3 q - 3 q^{8} + O(q^{10})$$ $$3 q - 3 q^{8} - 6 q^{29} + 3 q^{36} + 3 q^{50} + 3 q^{64} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(196))$$

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
196.1.b $$\chi_{196}(97, \cdot)$$ None 0 1
196.1.c $$\chi_{196}(99, \cdot)$$ 196.1.c.a 1 1
196.1.g $$\chi_{196}(67, \cdot)$$ 196.1.g.a 2 2
196.1.h $$\chi_{196}(117, \cdot)$$ None 0 2
196.1.k $$\chi_{196}(15, \cdot)$$ None 0 6
196.1.l $$\chi_{196}(13, \cdot)$$ None 0 6
196.1.n $$\chi_{196}(5, \cdot)$$ None 0 12
196.1.o $$\chi_{196}(11, \cdot)$$ None 0 12