# Properties

 Label 192.3.e Level $192$ Weight $3$ Character orbit 192.e Rep. character $\chi_{192}(65,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $6$ Sturm bound $96$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$192 = 2^{6} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 192.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$96$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(192, [\chi])$$.

Total New Old
Modular forms 76 18 58
Cusp forms 52 14 38
Eisenstein series 24 4 20

## Trace form

 $$14 q - 2 q^{9} + O(q^{10})$$ $$14 q - 2 q^{9} - 12 q^{13} + 20 q^{21} - 34 q^{25} + 84 q^{37} + 10 q^{49} + 60 q^{57} - 76 q^{61} - 256 q^{69} - 4 q^{73} - 146 q^{81} - 256 q^{85} + 308 q^{93} + 28 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(192, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.3.e.a $1$ $5.232$ $$\Q$$ $$\Q(\sqrt{-3})$$ $$0$$ $$-3$$ $$0$$ $$-2$$ $$q-3q^{3}-2q^{7}+9q^{9}+22q^{13}+26q^{19}+\cdots$$
192.3.e.b $1$ $5.232$ $$\Q$$ $$\Q(\sqrt{-3})$$ $$0$$ $$3$$ $$0$$ $$2$$ $$q+3q^{3}+2q^{7}+9q^{9}+22q^{13}-26q^{19}+\cdots$$
192.3.e.c $2$ $5.232$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-2$$ $$0$$ $$-12$$ $$q+(-1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+\cdots)q^{9}+\cdots$$
192.3.e.d $2$ $5.232$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$0$$ $$12$$ $$q+(1+\beta )q^{3}+2\beta q^{5}+6q^{7}+(-7+2\beta )q^{9}+\cdots$$
192.3.e.e $4$ $5.232$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\beta _{3})q^{7}+\cdots$$
192.3.e.f $4$ $5.232$ $$\Q(\sqrt{-2}, \sqrt{7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{5}+(\beta _{1}+2\beta _{3})q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(192, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(192, [\chi]) \simeq$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 2}$$