# Properties

 Label 136.1.j Level $136$ Weight $1$ Character orbit 136.j Rep. character $\chi_{136}(115,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $2$ Newform subspaces $1$ Sturm bound $18$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$136 = 2^{3} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 136.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$136$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$18$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(136, [\chi])$$.

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

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

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

## Trace form

 $$2q - 2q^{3} - 2q^{4} - 2q^{6} + O(q^{10})$$ $$2q - 2q^{3} - 2q^{4} - 2q^{6} + 2q^{11} + 2q^{12} + 2q^{16} + 2q^{18} - 2q^{22} + 2q^{24} - 4q^{33} - 2q^{34} + 4q^{38} - 2q^{41} - 2q^{44} - 2q^{48} + 2q^{50} - 2q^{51} + 4q^{57} - 2q^{64} - 2q^{72} - 2q^{73} + 2q^{75} + 2q^{81} + 2q^{82} + 2q^{88} - 2q^{96} + 2q^{97} - 2q^{98} + 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(136, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
136.1.j.a $$2$$ $$0.068$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}+(-1-i)q^{3}-q^{4}+(-1+i+\cdots)q^{6}+\cdots$$