# Properties

 Label 155.1.c Level $155$ Weight $1$ Character orbit 155.c Rep. character $\chi_{155}(154,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $2$ Sturm bound $16$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$155 = 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 155.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$155$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$16$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(155, [\chi])$$.

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

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 3 0 0 0

## Trace form

 $$3 q - 3 q^{4} - 3 q^{9} + O(q^{10})$$ $$3 q - 3 q^{4} - 3 q^{9} - 3 q^{10} + 6 q^{14} + 3 q^{16} - 3 q^{20} - 3 q^{31} + 3 q^{35} + 3 q^{36} + 3 q^{40} - 3 q^{49} - 3 q^{50} - 6 q^{56} + 3 q^{64} + 3 q^{70} - 6 q^{76} + 3 q^{81} + 3 q^{90} + 3 q^{95} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(155, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
155.1.c.a $$1$$ $$0.077$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-31})$$, $$\Q(\sqrt{-155})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$-1$$ $$0$$ $$q+q^{4}-q^{5}-q^{9}+q^{16}-2q^{19}-q^{20}+\cdots$$
155.1.c.b $$2$$ $$0.077$$ $$\Q(\sqrt{-3})$$ $$D_{6}$$ $$\Q(\sqrt{-31})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots$$