# Properties

 Label 378.2.v Level 378 Weight 2 Character orbit v Rep. character $$\chi_{378}(67,\cdot)$$ 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.v (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

 $$144q + 6q^{6} + 24q^{9} + O(q^{10})$$ $$144q + 6q^{6} + 24q^{9} + 24q^{11} - 6q^{14} - 12q^{15} - 24q^{17} - 30q^{21} + 42q^{23} - 36q^{26} + 6q^{29} + 18q^{30} - 36q^{33} - 36q^{35} + 6q^{36} - 72q^{39} - 12q^{41} + 48q^{42} + 6q^{45} + 18q^{47} + 36q^{49} + 12q^{50} - 36q^{51} - 30q^{53} - 36q^{54} - 6q^{56} - 6q^{57} - 60q^{59} + 18q^{60} + 18q^{61} - 48q^{62} - 60q^{63} - 72q^{64} + 54q^{65} + 18q^{68} - 60q^{69} - 18q^{70} + 24q^{71} - 12q^{72} + 72q^{73} - 36q^{74} + 12q^{75} - 30q^{77} + 36q^{78} - 36q^{79} - 12q^{80} + 48q^{81} - 6q^{84} + 72q^{85} - 24q^{86} - 156q^{87} - 72q^{89} + 36q^{91} + 42q^{92} - 96q^{93} - 36q^{94} - 30q^{95} - 24q^{98} + 36q^{99} + O(q^{100})$$

## 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.v.a $$72$$ $$3.018$$ None $$0$$ $$0$$ $$0$$ $$-6$$
378.2.v.b $$72$$ $$3.018$$ None $$0$$ $$0$$ $$0$$ $$6$$

## 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