Properties

 Label 378.2.g Level 378 Weight 2 Character orbit g Rep. character $$\chi_{378}(109,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 20 Newforms 8 Sturm bound 144 Trace bound 5

Related objects

Defining parameters

 Level: $$N$$ = $$378 = 2 \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 378.g (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$7$$ Character field: $$\Q(\zeta_{3})$$ Newforms: $$8$$ Sturm bound: $$144$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$, $$11$$

Dimensions

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

Total New Old
Modular forms 168 20 148
Cusp forms 120 20 100
Eisenstein series 48 0 48

Trace form

 $$20q$$ $$\mathstrut -\mathstrut 10q^{4}$$ $$\mathstrut -\mathstrut 14q^{7}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$20q$$ $$\mathstrut -\mathstrut 10q^{4}$$ $$\mathstrut -\mathstrut 14q^{7}$$ $$\mathstrut +\mathstrut 2q^{10}$$ $$\mathstrut +\mathstrut 12q^{13}$$ $$\mathstrut -\mathstrut 10q^{16}$$ $$\mathstrut +\mathstrut 16q^{19}$$ $$\mathstrut +\mathstrut 4q^{22}$$ $$\mathstrut -\mathstrut 8q^{25}$$ $$\mathstrut +\mathstrut 4q^{28}$$ $$\mathstrut -\mathstrut 12q^{31}$$ $$\mathstrut -\mathstrut 8q^{34}$$ $$\mathstrut -\mathstrut 14q^{37}$$ $$\mathstrut +\mathstrut 2q^{40}$$ $$\mathstrut +\mathstrut 100q^{43}$$ $$\mathstrut -\mathstrut 8q^{46}$$ $$\mathstrut +\mathstrut 38q^{49}$$ $$\mathstrut -\mathstrut 6q^{52}$$ $$\mathstrut -\mathstrut 104q^{55}$$ $$\mathstrut -\mathstrut 16q^{58}$$ $$\mathstrut -\mathstrut 18q^{61}$$ $$\mathstrut +\mathstrut 20q^{64}$$ $$\mathstrut -\mathstrut 10q^{67}$$ $$\mathstrut -\mathstrut 50q^{70}$$ $$\mathstrut -\mathstrut 16q^{73}$$ $$\mathstrut -\mathstrut 32q^{76}$$ $$\mathstrut -\mathstrut 18q^{79}$$ $$\mathstrut +\mathstrut 40q^{85}$$ $$\mathstrut -\mathstrut 2q^{88}$$ $$\mathstrut +\mathstrut 60q^{91}$$ $$\mathstrut -\mathstrut 24q^{94}$$ $$\mathstrut +\mathstrut 32q^{97}$$ $$\mathstrut +\mathstrut O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(378, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
378.2.g.a $$2$$ $$3.018$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-3$$ $$-4$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots$$
378.2.g.b $$2$$ $$3.018$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-3+2\zeta_{6})q^{7}+\cdots$$
378.2.g.c $$2$$ $$3.018$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$2$$ $$1$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots$$
378.2.g.d $$2$$ $$3.018$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-2$$ $$1$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots$$
378.2.g.e $$2$$ $$3.018$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$0$$ $$-4$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-3+2\zeta_{6})q^{7}+\cdots$$
378.2.g.f $$2$$ $$3.018$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$3$$ $$-4$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots$$
378.2.g.g $$4$$ $$3.018$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$-2$$ $$0$$ $$2$$ $$0$$ $$q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
378.2.g.h $$4$$ $$3.018$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$2$$ $$0$$ $$-2$$ $$0$$ $$q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(378, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 2}$$