# Properties

 Label 208.2.w Level $208$ Weight $2$ Character orbit 208.w Rep. character $\chi_{208}(17,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $3$ Sturm bound $56$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$208 = 2^{4} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 208.w (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$56$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 68 16 52
Cusp forms 44 12 32
Eisenstein series 24 4 20

## Trace form

 $$12 q - q^{3} + 9 q^{7} - 5 q^{9} + O(q^{10})$$ $$12 q - q^{3} + 9 q^{7} - 5 q^{9} + 3 q^{11} - q^{13} - 6 q^{15} + 3 q^{19} - 5 q^{23} - 6 q^{25} + 26 q^{27} - 2 q^{29} - 3 q^{33} - 16 q^{35} - 18 q^{37} - 5 q^{39} - 6 q^{41} + 7 q^{43} + 27 q^{45} - 9 q^{49} - 50 q^{51} + 2 q^{53} - 16 q^{55} - 39 q^{59} - 30 q^{63} + 5 q^{65} + 33 q^{67} - 3 q^{69} + 39 q^{71} + 21 q^{75} - 42 q^{77} - 32 q^{79} - 10 q^{81} + 15 q^{85} + 25 q^{87} - 3 q^{89} + 49 q^{91} + 30 q^{93} - 22 q^{95} + 21 q^{97} + O(q^{100})$$

## 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.w.a $2$ $1.661$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$3$$ $$q+(-1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots$$
208.2.w.b $2$ $1.661$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(2-2\zeta_{6})q^{3}+(1-2\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots$$
208.2.w.c $8$ $1.661$ 8.0.195105024.2 None $$0$$ $$-2$$ $$0$$ $$6$$ $$q+(\beta _{2}-\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(208, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 2}$$