## Defining parameters

 Level: $$N$$ = $$1156 = 2^{2} \cdot 17^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$7$$ Newform subspaces: $$10$$ Sturm bound: $$83232$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1156))$$.

Total New Old
Modular forms 1091 454 637
Cusp forms 91 85 6
Eisenstein series 1000 369 631

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 85 0 0 0

## Trace form

 $$85 q + q^{2} + q^{4} + 2 q^{5} + q^{8} + q^{9} + O(q^{10})$$ $$85 q + q^{2} + q^{4} + 2 q^{5} + q^{8} + q^{9} - 6 q^{10} + 2 q^{13} - 7 q^{16} - 7 q^{18} - 6 q^{20} - 5 q^{25} - 6 q^{26} - 6 q^{29} + q^{32} + q^{36} + 2 q^{37} + 2 q^{40} - 6 q^{41} - 6 q^{45} + q^{49} + 3 q^{50} - 14 q^{52} - 6 q^{53} + 2 q^{58} + 2 q^{61} + q^{64} - 4 q^{65} - 4 q^{68} - 7 q^{72} - 6 q^{73} - 6 q^{74} + 2 q^{80} + q^{81} - 6 q^{82} - 4 q^{85} + 2 q^{89} - 6 q^{90} + 2 q^{97} - 7 q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1156))$$

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
1156.1.c $$\chi_{1156}(579, \cdot)$$ 1156.1.c.a 1 1
1156.1.c.b 2
1156.1.d $$\chi_{1156}(1155, \cdot)$$ 1156.1.d.a 2 1
1156.1.f $$\chi_{1156}(251, \cdot)$$ 1156.1.f.a 2 2
1156.1.f.b 2
1156.1.g $$\chi_{1156}(155, \cdot)$$ 1156.1.g.a 4 4
1156.1.g.b 8
1156.1.j $$\chi_{1156}(65, \cdot)$$ None 0 8
1156.1.l $$\chi_{1156}(67, \cdot)$$ 1156.1.l.a 16 16
1156.1.m $$\chi_{1156}(35, \cdot)$$ 1156.1.m.a 16 16
1156.1.o $$\chi_{1156}(47, \cdot)$$ 1156.1.o.a 32 32
1156.1.r $$\chi_{1156}(15, \cdot)$$ None 0 64
1156.1.s $$\chi_{1156}(5, \cdot)$$ None 0 128

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1156))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1156)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 2}$$