# Properties

 Label 52.1.j Level $52$ Weight $1$ Character orbit 52.j Rep. character $\chi_{52}(3,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $2$ Newform subspaces $1$ Sturm bound $7$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$52 = 2^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 52.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$52$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$7$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(52, [\chi])$$.

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

 $$2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} - q^{9} + O(q^{10})$$ $$2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} - q^{9} + q^{10} - q^{13} - q^{16} + q^{17} + 2 q^{18} + q^{20} - q^{26} + q^{29} - q^{32} - 2 q^{34} - q^{36} + q^{37} - 2 q^{40} + q^{41} + q^{45} - q^{49} + 2 q^{52} - 2 q^{53} + q^{58} + q^{61} + 2 q^{64} + q^{65} + q^{68} - q^{72} - 2 q^{73} + q^{74} + q^{80} - q^{81} + q^{82} - q^{85} - 2 q^{89} - 2 q^{90} - 2 q^{97} - q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(52, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
52.1.j.a $2$ $0.026$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-1})$$ None $$-1$$ $$0$$ $$-2$$ $$0$$ $$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$$