# Properties

 Label 55.2.e Level $55$ Weight $2$ Character orbit 55.e Rep. character $\chi_{55}(32,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $8$ Newform subspaces $2$ Sturm bound $12$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$55 = 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 55.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$12$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

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

## Trace form

 $$8 q - 6 q^{3} - 8 q^{5} + O(q^{10})$$ $$8 q - 6 q^{3} - 8 q^{5} + 4 q^{11} + 8 q^{12} - 4 q^{15} - 12 q^{16} + 24 q^{20} - 20 q^{22} + 14 q^{23} + 14 q^{25} - 40 q^{26} + 6 q^{27} + 8 q^{31} - 26 q^{33} + 36 q^{36} - 2 q^{37} + 40 q^{38} - 22 q^{45} - 12 q^{47} + 4 q^{48} - 16 q^{53} + 14 q^{55} - 40 q^{58} - 64 q^{60} + 40 q^{66} + 38 q^{67} - 44 q^{71} + 36 q^{75} + 40 q^{78} - 8 q^{80} + 12 q^{81} + 40 q^{82} - 20 q^{88} + 48 q^{92} + 58 q^{93} - 62 q^{97} + O(q^{100})$$

## 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.e.a $4$ $0.439$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$-4$$ $$-8$$ $$0$$ $$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+3\beta _{2}q^{4}+\cdots$$
55.2.e.b $4$ $0.439$ $$\Q(i, \sqrt{11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{3})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$