# Properties

 Label 378.2.ba Level 378 Weight 2 Character orbit ba Rep. character $$\chi_{378}(47,\cdot)$$ 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.ba (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

 $$144q - 18q^{6} + 24q^{9} + O(q^{10})$$ $$144q - 18q^{6} + 24q^{9} - 24q^{11} + 6q^{14} + 12q^{15} - 30q^{21} - 42q^{23} - 6q^{29} - 18q^{30} + 6q^{36} + 48q^{39} - 48q^{42} + 18q^{45} - 54q^{47} - 36q^{49} + 12q^{50} - 36q^{51} - 90q^{53} + 6q^{56} - 6q^{57} + 18q^{60} + 54q^{61} - 24q^{63} + 72q^{64} + 78q^{65} - 72q^{66} - 54q^{68} + 36q^{69} - 18q^{70} - 72q^{71} + 12q^{72} - 36q^{74} - 6q^{77} - 60q^{78} + 36q^{79} - 6q^{84} - 72q^{85} + 24q^{86} + 36q^{91} - 42q^{92} + 96q^{93} - 66q^{95} - 108q^{99} + O(q^{100})$$

## 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.ba.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