# Properties

 Label 209.2.j Level $209$ Weight $2$ Character orbit 209.j Rep. character $\chi_{209}(23,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $96$ Newform subspaces $3$ Sturm bound $40$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$209 = 11 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 209.j (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$3$$ Sturm bound: $$40$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(209, [\chi])$$.

Total New Old
Modular forms 132 96 36
Cusp forms 108 96 12
Eisenstein series 24 0 24

## Trace form

 $$96 q - 12 q^{4} - 12 q^{6} + O(q^{10})$$ $$96 q - 12 q^{4} - 12 q^{6} - 30 q^{10} - 12 q^{12} - 6 q^{13} - 18 q^{14} - 42 q^{15} + 36 q^{16} - 6 q^{17} - 48 q^{18} + 12 q^{19} + 6 q^{21} - 24 q^{23} + 6 q^{24} - 12 q^{25} - 24 q^{27} - 12 q^{29} + 42 q^{30} - 30 q^{31} + 24 q^{32} - 60 q^{34} + 18 q^{35} + 12 q^{36} - 54 q^{38} + 24 q^{39} - 60 q^{40} + 24 q^{41} + 48 q^{42} + 6 q^{43} + 18 q^{45} + 30 q^{46} - 30 q^{47} + 84 q^{48} - 36 q^{49} + 18 q^{50} + 12 q^{51} + 48 q^{52} + 48 q^{53} + 24 q^{54} + 144 q^{56} - 30 q^{57} - 72 q^{58} - 54 q^{59} + 54 q^{60} + 30 q^{62} + 6 q^{63} + 6 q^{64} + 30 q^{65} - 30 q^{66} - 6 q^{67} + 6 q^{68} - 108 q^{70} + 54 q^{71} + 12 q^{72} - 78 q^{73} - 54 q^{74} - 84 q^{75} - 48 q^{76} - 102 q^{78} + 66 q^{79} + 54 q^{80} + 24 q^{81} + 96 q^{82} + 72 q^{84} + 48 q^{85} - 24 q^{86} - 60 q^{87} - 18 q^{88} - 24 q^{89} + 18 q^{90} + 96 q^{91} - 114 q^{92} - 48 q^{93} + 48 q^{94} - 6 q^{95} - 252 q^{96} + 42 q^{97} - 168 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(209, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
209.2.j.a $6$ $1.669$ $$\Q(\zeta_{18})$$ None $$3$$ $$0$$ $$6$$ $$6$$ $$q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots$$
209.2.j.b $42$ $1.669$ None $$-3$$ $$0$$ $$-6$$ $$-6$$
209.2.j.c $48$ $1.669$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(209, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(209, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 2}$$