# Properties

 Label 162.3.b Level $162$ Weight $3$ Character orbit 162.b Rep. character $\chi_{162}(161,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ Sturm bound $81$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 162.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$81$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(162, [\chi])$$.

Total New Old
Modular forms 66 8 58
Cusp forms 42 8 34
Eisenstein series 24 0 24

## Trace form

 $$8 q - 16 q^{4} + 4 q^{7} + O(q^{10})$$ $$8 q - 16 q^{4} + 4 q^{7} + 12 q^{10} - 44 q^{13} + 32 q^{16} + 16 q^{19} + 24 q^{22} + 20 q^{25} - 8 q^{28} - 44 q^{31} - 108 q^{34} + 52 q^{37} - 24 q^{40} + 4 q^{43} - 24 q^{46} + 276 q^{49} + 88 q^{52} - 324 q^{55} + 132 q^{58} - 176 q^{61} - 64 q^{64} + 172 q^{67} + 24 q^{70} + 16 q^{73} - 32 q^{76} + 76 q^{79} + 120 q^{82} - 396 q^{85} - 48 q^{88} + 500 q^{91} - 264 q^{94} + 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(162, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
162.3.b.a $4$ $4.414$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+\cdots$$
162.3.b.b $4$ $4.414$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\beta _{1}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}+(2+2\beta _{3})q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(162, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(162, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 2}$$