# Properties

 Label 155.2.b Level $155$ Weight $2$ Character orbit 155.b Rep. character $\chi_{155}(94,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $2$ Sturm bound $32$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$155 = 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 155.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$32$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(155, [\chi])$$.

Total New Old
Modular forms 18 14 4
Cusp forms 14 14 0
Eisenstein series 4 0 4

## Trace form

 $$14 q - 12 q^{4} + 4 q^{6} - 18 q^{9} + O(q^{10})$$ $$14 q - 12 q^{4} + 4 q^{6} - 18 q^{9} + q^{10} + 4 q^{11} + 6 q^{14} - 6 q^{15} - 8 q^{16} + 12 q^{19} - 21 q^{20} + 8 q^{21} + 28 q^{26} - 20 q^{29} - 30 q^{30} - 6 q^{31} + 32 q^{34} - 4 q^{35} + 44 q^{36} + 28 q^{39} + 14 q^{40} - 52 q^{44} + 12 q^{45} - 18 q^{49} - 29 q^{50} + 40 q^{51} - 4 q^{54} - 20 q^{55} + 12 q^{56} - 28 q^{60} - 16 q^{61} + 38 q^{64} + 2 q^{65} - 4 q^{69} - 5 q^{70} - 12 q^{71} - 16 q^{74} + 18 q^{75} - 30 q^{76} - 32 q^{79} + 25 q^{80} - 22 q^{81} + 40 q^{84} + 18 q^{85} + 72 q^{86} - 12 q^{89} - 29 q^{90} + 20 q^{91} + 40 q^{94} - 24 q^{95} - 60 q^{96} - 88 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(155, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
155.2.b.a $4$ $1.238$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{3})q^{2}-\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
155.2.b.b $10$ $1.238$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-1-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$$