## Defining parameters

 Level: $$N$$ = $$1161 = 3^{3} \cdot 43$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$6$$ Sturm bound: $$99792$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1161))$$.

Total New Old
Modular forms 1332 696 636
Cusp forms 72 40 32
Eisenstein series 1260 656 604

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 28 0 4 8

## Trace form

 $$40q - 4q^{4} + 2q^{7} + O(q^{10})$$ $$40q - 4q^{4} + 2q^{7} - 2q^{10} - 12q^{16} - 4q^{22} + 4q^{25} + 2q^{31} + 2q^{34} + 2q^{40} - 8q^{43} - 2q^{46} + 2q^{52} + 6q^{55} - 2q^{61} - 4q^{64} - 4q^{67} - 8q^{70} - 4q^{73} + 2q^{76} - 4q^{79} + 12q^{82} - 12q^{85} - 4q^{88} + 4q^{91} - 8q^{94} + 8q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1161))$$

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
1161.1.b $$\chi_{1161}(730, \cdot)$$ None 0 1
1161.1.c $$\chi_{1161}(431, \cdot)$$ None 0 1
1161.1.i $$\chi_{1161}(350, \cdot)$$ 1161.1.i.a 2 2
1161.1.i.b 4
1161.1.i.c 8
1161.1.j $$\chi_{1161}(136, \cdot)$$ 1161.1.j.a 2 2
1161.1.n $$\chi_{1161}(424, \cdot)$$ None 0 2
1161.1.o $$\chi_{1161}(638, \cdot)$$ None 0 2
1161.1.p $$\chi_{1161}(251, \cdot)$$ None 0 2
1161.1.q $$\chi_{1161}(44, \cdot)$$ None 0 2
1161.1.r $$\chi_{1161}(37, \cdot)$$ None 0 2
1161.1.s $$\chi_{1161}(343, \cdot)$$ None 0 2
1161.1.z $$\chi_{1161}(82, \cdot)$$ None 0 6
1161.1.ba $$\chi_{1161}(107, \cdot)$$ None 0 6
1161.1.be $$\chi_{1161}(221, \cdot)$$ None 0 6
1161.1.bf $$\chi_{1161}(85, \cdot)$$ None 0 6
1161.1.bg $$\chi_{1161}(173, \cdot)$$ None 0 6
1161.1.bh $$\chi_{1161}(7, \cdot)$$ None 0 6
1161.1.bi $$\chi_{1161}(265, \cdot)$$ None 0 6
1161.1.bj $$\chi_{1161}(92, \cdot)$$ None 0 6
1161.1.bp $$\chi_{1161}(35, \cdot)$$ None 0 12
1161.1.bq $$\chi_{1161}(143, \cdot)$$ None 0 12
1161.1.br $$\chi_{1161}(118, \cdot)$$ None 0 12
1161.1.bs $$\chi_{1161}(73, \cdot)$$ None 0 12
1161.1.bt $$\chi_{1161}(19, \cdot)$$ None 0 12
1161.1.bu $$\chi_{1161}(17, \cdot)$$ None 0 12
1161.1.by $$\chi_{1161}(53, \cdot)$$ 1161.1.by.a 12 12
1161.1.bz $$\chi_{1161}(28, \cdot)$$ 1161.1.bz.a 12 12
1161.1.cd $$\chi_{1161}(14, \cdot)$$ None 0 36
1161.1.ce $$\chi_{1161}(106, \cdot)$$ None 0 36
1161.1.cf $$\chi_{1161}(34, \cdot)$$ None 0 36
1161.1.cg $$\chi_{1161}(11, \cdot)$$ None 0 36
1161.1.ch $$\chi_{1161}(22, \cdot)$$ None 0 36
1161.1.ci $$\chi_{1161}(23, \cdot)$$ None 0 36

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1161))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1161)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(129))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(387))$$$$^{\oplus 2}$$