# Properties

 Label 208.2.f Level $208$ Weight $2$ Character orbit 208.f Rep. character $\chi_{208}(129,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $56$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$208 = 2^{4} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 208.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$56$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(208, [\chi])$$.

Total New Old
Modular forms 34 8 26
Cusp forms 22 6 16
Eisenstein series 12 2 10

## Trace form

 $$6 q + 4 q^{3} + 2 q^{9} + O(q^{10})$$ $$6 q + 4 q^{3} + 2 q^{9} - 2 q^{13} + 8 q^{23} - 6 q^{25} + 4 q^{27} - 4 q^{29} + 4 q^{35} - 16 q^{39} - 28 q^{43} - 18 q^{49} + 20 q^{51} + 4 q^{53} - 32 q^{55} + 12 q^{61} + 4 q^{65} - 24 q^{69} - 24 q^{75} + 24 q^{77} + 8 q^{79} - 26 q^{81} + 32 q^{87} + 20 q^{91} + 40 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(208, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
208.2.f.a $2$ $1.661$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+iq^{5}+iq^{7}-2q^{9}+(2-i)q^{13}+\cdots$$
208.2.f.b $4$ $1.661$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(208, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(208, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 2}$$