# Properties

 Label 136.1 Level 136 Weight 1 Dimension 7 Nonzero newspaces 3 Newform subspaces 3 Sturm bound 1152 Trace bound 1

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## Defining parameters

 Level: $$N$$ = $$136 = 2^{3} \cdot 17$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$3$$ Sturm bound: $$1152$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(136))$$.

Total New Old
Modular forms 109 37 72
Cusp forms 13 7 6
Eisenstein series 96 30 66

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 7 0 0 0

## Trace form

 $$7q - q^{2} - 2q^{3} - q^{4} - 2q^{6} - q^{8} - 3q^{9} + O(q^{10})$$ $$7q - q^{2} - 2q^{3} - q^{4} - 2q^{6} - q^{8} - 3q^{9} - 2q^{11} + 6q^{12} - q^{16} - q^{17} - 3q^{18} - 2q^{19} - 2q^{22} + 6q^{24} - q^{25} + 4q^{27} - q^{32} - 4q^{33} - q^{34} - 3q^{36} + 6q^{38} - 2q^{41} + 6q^{43} - 2q^{44} - 2q^{48} - q^{49} + 7q^{50} - 2q^{51} + 4q^{54} + 4q^{57} - 2q^{59} - q^{64} + 4q^{66} - 2q^{67} - q^{68} - 3q^{72} - 2q^{73} - 2q^{75} - 2q^{76} + 3q^{81} - 2q^{82} + 6q^{83} - 2q^{86} - 2q^{88} - 2q^{89} - 2q^{96} - 2q^{97} - q^{98} + 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(136))$$

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
136.1.d $$\chi_{136}(103, \cdot)$$ None 0 1
136.1.e $$\chi_{136}(67, \cdot)$$ 136.1.e.a 1 1
136.1.f $$\chi_{136}(35, \cdot)$$ None 0 1
136.1.g $$\chi_{136}(135, \cdot)$$ None 0 1
136.1.j $$\chi_{136}(115, \cdot)$$ 136.1.j.a 2 2
136.1.l $$\chi_{136}(47, \cdot)$$ None 0 2
136.1.m $$\chi_{136}(15, \cdot)$$ None 0 4
136.1.p $$\chi_{136}(19, \cdot)$$ 136.1.p.a 4 4
136.1.q $$\chi_{136}(5, \cdot)$$ None 0 8
136.1.t $$\chi_{136}(41, \cdot)$$ None 0 8

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(136))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(136)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 2}$$