# Properties

 Label 378.2.w Level 378 Weight 2 Character orbit w Rep. character $$\chi_{378}(25,\cdot)$$ Character field $$\Q(\zeta_{9})$$ Dimension 144 Newform subspaces 2 Sturm bound 144 Trace bound 7

# Related objects

## Defining parameters

 Level: $$N$$ = $$378 = 2 \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 378.w (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$189$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$2$$ Sturm bound: $$144$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$

## 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

 $$144q + 6q^{6} - 12q^{9} + O(q^{10})$$ $$144q + 6q^{6} - 12q^{9} - 12q^{11} - 6q^{14} - 12q^{15} + 48q^{17} + 6q^{21} + 6q^{23} - 36q^{26} + 6q^{29} + 18q^{30} - 36q^{33} + 18q^{35} + 6q^{36} + 54q^{39} - 12q^{41} - 24q^{42} - 12q^{45} + 18q^{47} - 18q^{49} + 12q^{50} + 18q^{51} - 30q^{53} + 18q^{54} + 12q^{56} - 6q^{57} + 30q^{59} - 36q^{60} - 36q^{61} - 48q^{62} - 60q^{63} - 72q^{64} - 108q^{65} - 72q^{66} - 36q^{68} - 60q^{69} - 18q^{70} + 24q^{71} - 12q^{72} - 36q^{73} + 18q^{74} - 6q^{75} - 102q^{77} + 36q^{78} - 36q^{79} - 12q^{80} - 24q^{81} - 6q^{84} + 72q^{85} - 24q^{86} - 66q^{87} + 144q^{89} - 18q^{91} + 42q^{92} + 12q^{93} - 36q^{94} + 114q^{95} + 12q^{98} + 36q^{99} + O(q^{100})$$

## 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.w.a $$72$$ $$3.018$$ None $$0$$ $$0$$ $$0$$ $$-3$$
378.2.w.b $$72$$ $$3.018$$ None $$0$$ $$0$$ $$0$$ $$3$$

## 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