# Properties

 Label 189.2.c Level $189$ Weight $2$ Character orbit 189.c Rep. character $\chi_{189}(188,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $3$ Sturm bound $48$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$189 = 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 189.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$48$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 30 10 20
Cusp forms 18 10 8
Eisenstein series 12 0 12

## Trace form

 $$10 q - 8 q^{4} - 3 q^{7} + O(q^{10})$$ $$10 q - 8 q^{4} - 3 q^{7} - 12 q^{16} - 28 q^{22} + 22 q^{25} + 26 q^{28} - 6 q^{37} + 12 q^{43} - 4 q^{46} - 29 q^{49} + 80 q^{58} + 36 q^{64} - 22 q^{67} - 36 q^{70} - 10 q^{79} - 36 q^{85} + 4 q^{88} + 27 q^{91} + O(q^{100})$$

## 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.c.a $2$ $1.509$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$1$$ $$q+2q^{4}+\zeta_{6}q^{7}+(1-2\zeta_{6})q^{13}+4q^{16}+\cdots$$
189.2.c.b $4$ $1.509$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{1}q^{2}-3q^{4}-\beta _{3}q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots$$
189.2.c.c $4$ $1.509$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{1}q^{2}-\beta _{2}q^{5}+(1-\beta _{3})q^{7}-2\beta _{1}q^{8}+\cdots$$

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

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