# Properties

 Label 189.2.e Level $189$ Weight $2$ Character orbit 189.e Rep. character $\chi_{189}(109,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $22$ Newform subspaces $6$ Sturm bound $48$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$189 = 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 189.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$6$$ Sturm bound: $$48$$ Trace bound: $$2$$ 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 22 38
Cusp forms 36 22 14
Eisenstein series 24 0 24

## Trace form

 $$22 q - 12 q^{4} + 9 q^{7} + O(q^{10})$$ $$22 q - 12 q^{4} + 9 q^{7} - 2 q^{10} - 30 q^{16} - 9 q^{19} + 40 q^{22} - 15 q^{25} - 20 q^{28} + 13 q^{31} + 4 q^{37} - 70 q^{43} - 18 q^{46} - 11 q^{49} + 20 q^{52} + 32 q^{55} + 4 q^{58} + 15 q^{61} + 112 q^{64} - 30 q^{67} + 152 q^{70} + 7 q^{73} - 76 q^{76} - 22 q^{79} - 118 q^{82} - 36 q^{85} - 54 q^{88} - 52 q^{91} + 30 q^{94} - 14 q^{97} + O(q^{100})$$

## 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.e.a $2$ $1.509$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$4$$ $$4$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$$
189.2.e.b $2$ $1.509$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-1$$ $$q+(2-2\zeta_{6})q^{4}+(1-3\zeta_{6})q^{7}+2q^{13}+\cdots$$
189.2.e.c $2$ $1.509$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-4$$ $$4$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$$
189.2.e.d $4$ $1.509$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-\beta _{2}q^{2}+(-4+4\beta _{1})q^{4}-\beta _{2}q^{5}+\cdots$$
189.2.e.e $6$ $1.509$ 6.0.309123.1 None $$-2$$ $$0$$ $$-1$$ $$2$$ $$q+(-\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(-2+\beta _{2}+\cdots)q^{4}+\cdots$$
189.2.e.f $6$ $1.509$ 6.0.309123.1 None $$2$$ $$0$$ $$1$$ $$2$$ $$q+(1-\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(189, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$