# Properties

 Label 162.4.c Level $162$ Weight $4$ Character orbit 162.c Rep. character $\chi_{162}(55,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $24$ Newform subspaces $10$ Sturm bound $108$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 162.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$10$$ Sturm bound: $$108$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(162, [\chi])$$.

Total New Old
Modular forms 186 24 162
Cusp forms 138 24 114
Eisenstein series 48 0 48

## Trace form

 $$24q - 48q^{4} - 60q^{7} + O(q^{10})$$ $$24q - 48q^{4} - 60q^{7} + 120q^{13} - 192q^{16} - 780q^{19} + 36q^{22} - 12q^{25} + 480q^{28} - 78q^{31} - 180q^{34} - 1392q^{37} - 132q^{43} - 1008q^{46} + 1008q^{49} + 480q^{52} + 4644q^{55} - 1260q^{58} + 84q^{61} + 1536q^{64} - 1914q^{67} - 540q^{70} - 924q^{73} + 1560q^{76} + 4602q^{79} + 3024q^{82} + 1026q^{85} + 144q^{88} - 5196q^{91} - 1224q^{94} + 120q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(162, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
162.4.c.a $$2$$ $$9.558$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-12$$ $$7$$ $$q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-12\zeta_{6}q^{5}+\cdots$$
162.4.c.b $$2$$ $$9.558$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-3$$ $$-29$$ $$q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots$$
162.4.c.c $$2$$ $$9.558$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$6$$ $$16$$ $$q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+6\zeta_{6}q^{5}+\cdots$$
162.4.c.d $$2$$ $$9.558$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$21$$ $$-8$$ $$q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+21\zeta_{6}q^{5}+\cdots$$
162.4.c.e $$2$$ $$9.558$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-21$$ $$-8$$ $$q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-21\zeta_{6}q^{5}+\cdots$$
162.4.c.f $$2$$ $$9.558$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-6$$ $$16$$ $$q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-6\zeta_{6}q^{5}+\cdots$$
162.4.c.g $$2$$ $$9.558$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$3$$ $$-29$$ $$q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots$$
162.4.c.h $$2$$ $$9.558$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$12$$ $$7$$ $$q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+12\zeta_{6}q^{5}+\cdots$$
162.4.c.i $$4$$ $$9.558$$ $$\Q(\zeta_{12})$$ None $$-4$$ $$0$$ $$-12$$ $$-16$$ $$q+(-2+2\zeta_{12})q^{2}-4\zeta_{12}q^{4}+(-6\zeta_{12}+\cdots)q^{5}+\cdots$$
162.4.c.j $$4$$ $$9.558$$ $$\Q(\zeta_{12})$$ None $$4$$ $$0$$ $$12$$ $$-16$$ $$q+(2-2\zeta_{12})q^{2}-4\zeta_{12}q^{4}+(6\zeta_{12}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(162, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(162, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 2}$$