# Properties

 Label 1183.1 Level 1183 Weight 1 Dimension 60 Nonzero newspaces 7 Newform subspaces 9 Sturm bound 113568 Trace bound 16

## Defining parameters

 Level: $$N$$ = $$1183 = 7 \cdot 13^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$7$$ Newform subspaces: $$9$$ Sturm bound: $$113568$$ Trace bound: $$16$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1183))$$.

Total New Old
Modular forms 1428 1083 345
Cusp forms 60 60 0
Eisenstein series 1368 1023 345

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 36 24 0 0

## Trace form

 $$60q + O(q^{10})$$ $$60q - 24q^{14} - 24q^{27} + 12q^{40} - 24q^{53} + 12q^{66} - 36q^{92} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1183))$$

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
1183.1.b $$\chi_{1183}(1182, \cdot)$$ 1183.1.b.a 6 1
1183.1.d $$\chi_{1183}(846, \cdot)$$ 1183.1.d.a 3 1
1183.1.d.b 3
1183.1.j $$\chi_{1183}(99, \cdot)$$ None 0 2
1183.1.l $$\chi_{1183}(530, \cdot)$$ None 0 2
1183.1.m $$\chi_{1183}(698, \cdot)$$ None 0 2
1183.1.n $$\chi_{1183}(146, \cdot)$$ 1183.1.n.a 6 2
1183.1.n.b 6
1183.1.o $$\chi_{1183}(339, \cdot)$$ None 0 2
1183.1.p $$\chi_{1183}(192, \cdot)$$ None 0 2
1183.1.s $$\chi_{1183}(675, \cdot)$$ None 0 2
1183.1.t $$\chi_{1183}(699, \cdot)$$ 1183.1.t.a 12 2
1183.1.v $$\chi_{1183}(360, \cdot)$$ None 0 2
1183.1.x $$\chi_{1183}(319, \cdot)$$ 1183.1.x.a 8 4
1183.1.y $$\chi_{1183}(526, \cdot)$$ None 0 4
1183.1.z $$\chi_{1183}(268, \cdot)$$ 1183.1.z.a 8 4
1183.1.bd $$\chi_{1183}(249, \cdot)$$ 1183.1.bd.a 8 4
1183.1.bf $$\chi_{1183}(27, \cdot)$$ None 0 12
1183.1.bh $$\chi_{1183}(90, \cdot)$$ None 0 12
1183.1.bm $$\chi_{1183}(8, \cdot)$$ None 0 24
1183.1.bo $$\chi_{1183}(68, \cdot)$$ None 0 24
1183.1.bq $$\chi_{1183}(62, \cdot)$$ None 0 24
1183.1.br $$\chi_{1183}(12, \cdot)$$ None 0 24
1183.1.bu $$\chi_{1183}(10, \cdot)$$ None 0 24
1183.1.bv $$\chi_{1183}(40, \cdot)$$ None 0 24
1183.1.bw $$\chi_{1183}(48, \cdot)$$ None 0 24
1183.1.bx $$\chi_{1183}(3, \cdot)$$ None 0 24
1183.1.by $$\chi_{1183}(17, \cdot)$$ None 0 24
1183.1.ca $$\chi_{1183}(11, \cdot)$$ None 0 48
1183.1.ce $$\chi_{1183}(18, \cdot)$$ None 0 48
1183.1.cf $$\chi_{1183}(15, \cdot)$$ None 0 48
1183.1.cg $$\chi_{1183}(2, \cdot)$$ None 0 48