# Properties

 Label 55.2.b Level $55$ Weight $2$ Character orbit 55.b Rep. character $\chi_{55}(34,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$55 = 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 55.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(55, [\chi])$$.

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

## Trace form

 $$4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9} + O(q^{10})$$ $$4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9} - 10 q^{10} - 4 q^{11} + 12 q^{14} + q^{15} + 14 q^{16} - 16 q^{19} - 12 q^{20} + 12 q^{21} + 4 q^{24} + q^{25} - 12 q^{29} - 6 q^{30} + 2 q^{31} + 16 q^{34} + 18 q^{35} - 30 q^{36} + 28 q^{40} + 12 q^{41} + 6 q^{44} + 18 q^{45} - 8 q^{46} - 20 q^{49} - 18 q^{50} - 28 q^{51} + 20 q^{54} + 3 q^{55} - 60 q^{56} + 18 q^{59} - 18 q^{60} + 20 q^{61} - 2 q^{64} - 8 q^{66} + 14 q^{69} + 24 q^{70} - 6 q^{71} + 12 q^{74} + 15 q^{75} + 24 q^{76} - 28 q^{79} + 6 q^{80} - 8 q^{81} + 48 q^{84} + 2 q^{85} - 12 q^{86} + 6 q^{89} - 28 q^{90} - 44 q^{94} + 12 q^{95} + 36 q^{96} + 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(55, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
55.2.b.a $4$ $0.439$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(\beta _{1}-\beta _{3})q^{3}+\cdots$$