## Defining parameters

 Level: $$N$$ = $$2563 = 11 \cdot 233$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newforms: $$6$$ Sturm bound: $$542880$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2563))$$.

Total New Old
Modular forms 2334 2092 242
Cusp forms 14 14 0
Eisenstein series 2320 2078 242

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 12 0

## Trace form

 $$14q - 4q^{3} - 2q^{4} + 4q^{5} - 2q^{9} + O(q^{10})$$ $$14q - 4q^{3} - 2q^{4} + 4q^{5} - 2q^{9} + 4q^{12} + 8q^{15} - 2q^{16} + 4q^{20} + 4q^{22} - 14q^{23} - 2q^{25} - 6q^{31} + 4q^{34} + 6q^{36} + 10q^{37} - 8q^{38} + 4q^{45} - 4q^{47} + 4q^{48} - 2q^{49} + 4q^{53} - 8q^{58} - 8q^{60} + 14q^{64} - 8q^{66} - 8q^{67} + 4q^{69} - 6q^{71} - 4q^{75} + 8q^{78} + 4q^{80} - 2q^{81} + 4q^{82} + 4q^{86} + 2q^{89} + 2q^{92} + 4q^{93} - 4q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2563))$$

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
2563.1.b $$\chi_{2563}(2562, \cdot)$$ 2563.1.b.a 1 1
2563.1.b.b 1
2563.1.b.c 2
2563.1.b.d 2
2563.1.c $$\chi_{2563}(2331, \cdot)$$ None 0 1
2563.1.e $$\chi_{2563}(2419, \cdot)$$ 2563.1.e.a 4 2
2563.1.e.b 4
2563.1.i $$\chi_{2563}(12, \cdot)$$ None 0 4
2563.1.k $$\chi_{2563}(700, \cdot)$$ None 0 4
2563.1.l $$\chi_{2563}(931, \cdot)$$ None 0 4
2563.1.n $$\chi_{2563}(788, \cdot)$$ None 0 8
2563.1.p $$\chi_{2563}(97, \cdot)$$ None 0 16
2563.1.s $$\chi_{2563}(32, \cdot)$$ None 0 28
2563.1.t $$\chi_{2563}(98, \cdot)$$ None 0 28
2563.1.v $$\chi_{2563}(109, \cdot)$$ None 0 56
2563.1.x $$\chi_{2563}(34, \cdot)$$ None 0 112
2563.1.z $$\chi_{2563}(29, \cdot)$$ None 0 112
2563.1.ba $$\chi_{2563}(2, \cdot)$$ None 0 112
2563.1.bc $$\chi_{2563}(7, \cdot)$$ None 0 224
2563.1.bf $$\chi_{2563}(3, \cdot)$$ None 0 448