# Properties

 Label 536.1 Level 536 Weight 1 Dimension 38 Nonzero newspaces 4 Newform subspaces 5 Sturm bound 17952 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$536 = 2^{3} \cdot 67$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$17952$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(536))$$.

Total New Old
Modular forms 436 168 268
Cusp forms 40 38 2
Eisenstein series 396 130 266

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 38 0 0 0

## Trace form

 $$38q - q^{2} - 2q^{3} + 5q^{4} - 4q^{6} - q^{8} + q^{9} + O(q^{10})$$ $$38q - q^{2} - 2q^{3} + 5q^{4} - 4q^{6} - q^{8} + q^{9} - 2q^{10} - 2q^{11} - 2q^{12} - 4q^{15} + 5q^{16} - 4q^{17} - 3q^{18} - 2q^{19} - 4q^{22} - 2q^{23} - 4q^{24} + 3q^{25} - 2q^{26} - 4q^{27} - q^{32} - 8q^{33} - 2q^{34} + q^{36} - 2q^{38} - 4q^{39} - 2q^{40} - 2q^{41} - 2q^{43} - 2q^{44} - 2q^{47} - 2q^{48} + 5q^{49} - q^{50} - 4q^{51} + 25q^{54} - 4q^{55} - 4q^{57} - 2q^{59} - 4q^{60} + 5q^{64} - 4q^{65} - 4q^{66} - q^{67} - 4q^{68} - 2q^{71} - 3q^{72} - 4q^{73} - 2q^{75} - 2q^{76} - 3q^{81} + 31q^{82} - 2q^{83} - 4q^{86} - 4q^{88} - 4q^{89} - 6q^{90} - 2q^{92} - 4q^{96} - 2q^{97} - q^{98} - 6q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(536))$$

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
536.1.b $$\chi_{536}(401, \cdot)$$ None 0 1
536.1.d $$\chi_{536}(135, \cdot)$$ None 0 1
536.1.f $$\chi_{536}(403, \cdot)$$ None 0 1
536.1.h $$\chi_{536}(133, \cdot)$$ 536.1.h.a 3 1
536.1.h.b 3
536.1.k $$\chi_{536}(97, \cdot)$$ None 0 2
536.1.m $$\chi_{536}(431, \cdot)$$ None 0 2
536.1.o $$\chi_{536}(163, \cdot)$$ 536.1.o.a 2 2
536.1.p $$\chi_{536}(365, \cdot)$$ None 0 2
536.1.r $$\chi_{536}(5, \cdot)$$ None 0 10
536.1.t $$\chi_{536}(59, \cdot)$$ 536.1.t.a 10 10
536.1.v $$\chi_{536}(15, \cdot)$$ None 0 10
536.1.x $$\chi_{536}(137, \cdot)$$ None 0 10
536.1.z $$\chi_{536}(13, \cdot)$$ None 0 20
536.1.ba $$\chi_{536}(19, \cdot)$$ 536.1.ba.a 20 20
536.1.bc $$\chi_{536}(23, \cdot)$$ None 0 20
536.1.be $$\chi_{536}(41, \cdot)$$ None 0 20

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(536))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(536)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(268))$$$$^{\oplus 2}$$