# Properties

 Label 297.1 Level 297 Weight 1 Dimension 8 Nonzero newspaces 2 Newform subspaces 2 Sturm bound 6480 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$297 = 3^{3} \cdot 11$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$6480$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(297))$$.

Total New Old
Modular forms 312 152 160
Cusp forms 12 8 4
Eisenstein series 300 144 156

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 8 0 0 0

## Trace form

 $$8 q - q^{4} - 4 q^{5} + O(q^{10})$$ $$8 q - q^{4} - 4 q^{5} + q^{11} - 3 q^{15} - q^{16} + 5 q^{20} + 2 q^{23} - 3 q^{25} - 3 q^{27} - 2 q^{31} - 3 q^{33} + 6 q^{36} - 2 q^{37} - 5 q^{44} - 4 q^{47} - 3 q^{48} - q^{49} + 2 q^{53} - 2 q^{55} - 4 q^{59} - q^{64} + 7 q^{67} + 2 q^{71} + 6 q^{75} + 2 q^{80} - q^{89} + 2 q^{92} + 6 q^{93} + 7 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(297))$$

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
297.1.b $$\chi_{297}(188, \cdot)$$ None 0 1
297.1.c $$\chi_{297}(109, \cdot)$$ None 0 1
297.1.h $$\chi_{297}(10, \cdot)$$ 297.1.h.a 2 2
297.1.i $$\chi_{297}(89, \cdot)$$ None 0 2
297.1.l $$\chi_{297}(28, \cdot)$$ None 0 4
297.1.m $$\chi_{297}(26, \cdot)$$ None 0 4
297.1.p $$\chi_{297}(23, \cdot)$$ None 0 6
297.1.q $$\chi_{297}(43, \cdot)$$ 297.1.q.a 6 6
297.1.r $$\chi_{297}(71, \cdot)$$ None 0 8
297.1.s $$\chi_{297}(19, \cdot)$$ None 0 8
297.1.v $$\chi_{297}(5, \cdot)$$ None 0 24
297.1.w $$\chi_{297}(7, \cdot)$$ None 0 24

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(297))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(297)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 2}$$