# Properties

 Label 57.2.d Level $57$ Weight $2$ Character orbit 57.d Rep. character $\chi_{57}(56,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $13$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$57 = 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 57.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$13$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(57, [\chi])$$.

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

## Trace form

 $$4 q - 4 q^{6} + 4 q^{7} - 8 q^{9} + O(q^{10})$$ $$4 q - 4 q^{6} + 4 q^{7} - 8 q^{9} - 16 q^{16} + 12 q^{19} + 8 q^{24} + 20 q^{30} + 20 q^{39} - 4 q^{42} - 20 q^{43} - 20 q^{45} - 24 q^{49} + 28 q^{54} + 20 q^{55} - 20 q^{57} - 32 q^{58} - 4 q^{61} - 8 q^{63} + 32 q^{64} - 20 q^{66} - 12 q^{73} - 4 q^{81} + 56 q^{82} + 60 q^{85} + 16 q^{87} - 20 q^{93} + 20 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(57, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
57.2.d.a $4$ $0.455$ $$\Q(\sqrt{2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{2}q^{2}-\beta _{1}q^{3}+\beta _{3}q^{5}+(-1-\beta _{3})q^{6}+\cdots$$