# Properties

 Label 162.4.e Level 162 Weight 4 Character orbit e Rep. character $$\chi_{162}(19,\cdot)$$ Character field $$\Q(\zeta_{9})$$ Dimension 54 Newform subspaces 2 Sturm bound 108 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 162.e (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$27$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$2$$ Sturm bound: $$108$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 522 54 468
Cusp forms 450 54 396
Eisenstein series 72 0 72

## Trace form

 $$54q + 24q^{5} - 24q^{8} + O(q^{10})$$ $$54q + 24q^{5} - 24q^{8} + 51q^{11} + 132q^{14} - 204q^{17} - 192q^{20} + 54q^{22} + 660q^{23} + 432q^{25} + 936q^{26} + 762q^{29} + 108q^{31} - 270q^{34} - 1248q^{35} - 672q^{38} - 2019q^{41} - 513q^{43} - 264q^{44} - 162q^{47} + 594q^{49} + 792q^{50} + 3588q^{53} + 528q^{56} + 462q^{59} - 54q^{61} - 1488q^{62} - 1728q^{64} - 9384q^{65} + 2511q^{67} - 1032q^{68} + 1080q^{70} - 240q^{71} + 432q^{73} + 3084q^{74} - 1080q^{76} + 10308q^{77} - 5616q^{79} + 960q^{80} + 4698q^{83} - 4320q^{85} + 3618q^{86} - 432q^{88} - 3669q^{89} - 540q^{91} - 2256q^{92} + 3672q^{94} - 13902q^{95} + 6885q^{97} - 5358q^{98} + O(q^{100})$$

## 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.e.a $$24$$ $$9.558$$ None $$0$$ $$0$$ $$12$$ $$-33$$
162.4.e.b $$30$$ $$9.558$$ None $$0$$ $$0$$ $$12$$ $$33$$

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

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

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database