# Properties

 Label 189.2.h Level $189$ Weight $2$ Character orbit 189.h Rep. character $\chi_{189}(37,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $12$ Newform subspaces $2$ Sturm bound $48$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$189 = 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 189.h (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(189, [\chi])$$.

Total New Old
Modular forms 60 20 40
Cusp forms 36 12 24
Eisenstein series 24 8 16

## Trace form

 $$12 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 12 q^{8} + O(q^{10})$$ $$12 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 12 q^{8} - 6 q^{10} + q^{11} - 3 q^{13} + 16 q^{14} - 6 q^{16} - 9 q^{17} - 4 q^{20} - 6 q^{22} + 3 q^{25} - 16 q^{26} - 6 q^{28} - 8 q^{29} + 6 q^{31} - 14 q^{32} - 4 q^{35} - 3 q^{37} - 19 q^{38} - 6 q^{40} - 10 q^{41} - 6 q^{43} + 5 q^{44} + 54 q^{47} - 6 q^{49} - 23 q^{50} - 15 q^{52} + 12 q^{53} - 6 q^{55} - 6 q^{56} - 9 q^{58} + 60 q^{59} + 12 q^{62} - 36 q^{64} - 32 q^{65} + 12 q^{67} - 30 q^{68} + 39 q^{70} + 30 q^{71} + 12 q^{73} + 39 q^{74} + 6 q^{76} + 14 q^{77} + 24 q^{79} - 19 q^{80} - 18 q^{83} - 3 q^{85} + 7 q^{86} - 3 q^{88} - 41 q^{89} + 21 q^{91} - 30 q^{92} + 6 q^{94} - 26 q^{95} - 3 q^{97} - 61 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(189, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
189.2.h.a $2$ $1.509$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-1$$ $$4$$ $$q-q^{2}-q^{4}+(-1+\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
189.2.h.b $10$ $1.509$ 10.0.$$\cdots$$.1 None $$4$$ $$0$$ $$-4$$ $$-4$$ $$q+(\beta _{1}-\beta _{5})q^{2}+(1+\beta _{3})q^{4}+(\beta _{6}-\beta _{9})q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(189, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(189, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$