# Properties

 Label 171.2.d Level $171$ Weight $2$ Character orbit 171.d Rep. character $\chi_{171}(170,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ Sturm bound $40$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$171 = 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 171.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$40$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(171, [\chi])$$.

Total New Old
Modular forms 24 8 16
Cusp forms 16 8 8
Eisenstein series 8 0 8

## Trace form

 $$8 q + 4 q^{4} - 8 q^{7} + O(q^{10})$$ $$8 q + 4 q^{4} - 8 q^{7} + 12 q^{16} - 12 q^{19} - 8 q^{25} - 24 q^{28} + 12 q^{43} + 36 q^{49} - 20 q^{55} + 40 q^{58} + 32 q^{61} - 84 q^{64} + 68 q^{73} - 36 q^{76} - 40 q^{82} - 76 q^{85} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(171, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
171.2.d.a $4$ $1.365$ $$\Q(\sqrt{-2}, \sqrt{19})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-2q^{4}+\beta _{1}q^{5}+\beta _{3}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$$
171.2.d.b $4$ $1.365$ $$\Q(\sqrt{-2}, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{3}q^{2}+3q^{4}-\beta _{1}q^{5}-2q^{7}-\beta _{3}q^{8}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(171, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(171, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 2}$$