Properties

 Label 891.2.e Level $891$ Weight $2$ Character orbit 891.e Rep. character $\chi_{891}(298,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $80$ Newform subspaces $22$ Sturm bound $216$ Trace bound $7$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$891 = 3^{4} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 891.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$22$$ Sturm bound: $$216$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$2$$, $$5$$, $$7$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(891, [\chi])$$.

Total New Old
Modular forms 240 80 160
Cusp forms 192 80 112
Eisenstein series 48 0 48

Trace form

 $$80 q - 40 q^{4} + 10 q^{7} + O(q^{10})$$ $$80 q - 40 q^{4} + 10 q^{7} + 10 q^{13} - 40 q^{16} - 20 q^{19} - 46 q^{25} - 80 q^{28} + 34 q^{31} + 60 q^{34} - 8 q^{37} + 60 q^{40} + 40 q^{43} - 72 q^{46} - 54 q^{49} + 4 q^{52} + 12 q^{55} - 36 q^{58} - 26 q^{61} + 32 q^{64} - 8 q^{67} - 24 q^{70} + 4 q^{73} + 100 q^{76} + 10 q^{79} + 48 q^{82} + 12 q^{85} - 76 q^{91} - 60 q^{94} + 16 q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(891, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
891.2.e.a $2$ $7.115$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-2$$ $$-1$$ $$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$$
891.2.e.b $2$ $7.115$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$1$$ $$2$$ $$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$$
891.2.e.c $2$ $7.115$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-4$$ $$2$$ $$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots$$
891.2.e.d $2$ $7.115$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-1$$ $$2$$ $$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots$$
891.2.e.e $2$ $7.115$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$2$$ $$-4$$ $$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$$
891.2.e.f $2$ $7.115$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$2$$ $$5$$ $$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$$
891.2.e.g $2$ $7.115$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-2$$ $$-4$$ $$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots$$
891.2.e.h $2$ $7.115$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-2$$ $$5$$ $$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(5+\cdots)q^{7}+\cdots$$
891.2.e.i $2$ $7.115$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$1$$ $$2$$ $$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots$$
891.2.e.j $2$ $7.115$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$4$$ $$2$$ $$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+4\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots$$
891.2.e.k $2$ $7.115$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-1$$ $$2$$ $$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots$$
891.2.e.l $2$ $7.115$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$2$$ $$-1$$ $$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$$
891.2.e.m $4$ $7.115$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$-2$$ $$4$$ $$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots$$
891.2.e.n $4$ $7.115$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None $$-1$$ $$0$$ $$-1$$ $$0$$ $$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$$
891.2.e.o $4$ $7.115$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None $$1$$ $$0$$ $$1$$ $$0$$ $$q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$$
891.2.e.p $4$ $7.115$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$2$$ $$4$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
891.2.e.q $6$ $7.115$ 6.0.954288.1 None $$-1$$ $$0$$ $$2$$ $$-7$$ $$q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots$$
891.2.e.r $6$ $7.115$ 6.0.2101707.2 None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots$$
891.2.e.s $6$ $7.115$ 6.0.2101707.2 None $$0$$ $$0$$ $$6$$ $$0$$ $$q+(\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots$$
891.2.e.t $6$ $7.115$ 6.0.954288.1 None $$1$$ $$0$$ $$-2$$ $$-7$$ $$q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
891.2.e.u $8$ $7.115$ 8.0.22581504.2 None $$-2$$ $$0$$ $$-8$$ $$2$$ $$q+(-1+\beta _{1}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
891.2.e.v $8$ $7.115$ 8.0.22581504.2 None $$2$$ $$0$$ $$8$$ $$2$$ $$q+(1-\beta _{1}-\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{4}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(891, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(891, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(99, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(297, [\chi])$$$$^{\oplus 2}$$