# Properties

 Label 378.2.z Level 378 Weight 2 Character orbit z Rep. character $$\chi_{378}(41,\cdot)$$ Character field $$\Q(\zeta_{18})$$ Dimension 144 Newform subspaces 1 Sturm bound 144 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$378 = 2 \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 378.z (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$189$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$1$$ Sturm bound: $$144$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(378, [\chi])$$.

Total New Old
Modular forms 456 144 312
Cusp forms 408 144 264
Eisenstein series 48 0 48

## Trace form

 $$144q - 12q^{9} + O(q^{10})$$ $$144q - 12q^{9} + 12q^{11} + 6q^{14} + 12q^{15} + 24q^{21} - 60q^{23} + 12q^{29} - 72q^{30} + 54q^{35} - 12q^{36} + 48q^{39} + 24q^{42} + 18q^{49} - 60q^{50} - 36q^{51} + 6q^{56} - 60q^{57} - 36q^{60} - 78q^{63} + 72q^{64} - 120q^{65} + 36q^{70} - 72q^{71} - 24q^{72} - 36q^{74} + 66q^{77} - 60q^{78} - 72q^{79} + 12q^{84} - 72q^{85} - 48q^{86} - 18q^{91} + 12q^{92} + 24q^{93} - 120q^{95} + 36q^{98} + 144q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(378, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
378.2.z.a $$144$$ $$3.018$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(378, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(378, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database