# Properties

 Label 171.1.c Level $171$ Weight $1$ Character orbit 171.c Rep. character $\chi_{171}(37,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $20$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$171 = 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 171.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$20$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(171, [\chi])$$.

Total New Old
Modular forms 5 2 3
Cusp forms 1 1 0
Eisenstein series 4 1 3

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q + q^{4} - 2 q^{7} + O(q^{10})$$ $$q + q^{4} - 2 q^{7} + q^{16} - q^{19} - q^{25} - 2 q^{28} + 2 q^{43} + 3 q^{49} - 2 q^{61} + q^{64} + 2 q^{73} - q^{76} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(171, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
171.1.c.a $1$ $0.085$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-19})$$ $$\Q(\sqrt{57})$$ $$0$$ $$0$$ $$0$$ $$-2$$ $$q+q^{4}-2q^{7}+q^{16}-q^{19}-q^{25}+\cdots$$