# Properties

 Label 1386.2.bk Level $1386$ Weight $2$ Character orbit 1386.bk Rep. character $\chi_{1386}(703,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $80$ Newform subspaces $4$ Sturm bound $576$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.bk (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$576$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1386, [\chi])$$.

Total New Old
Modular forms 608 80 528
Cusp forms 544 80 464
Eisenstein series 64 0 64

## Trace form

 $$80q + 40q^{4} - 12q^{5} + O(q^{10})$$ $$80q + 40q^{4} - 12q^{5} - 8q^{14} - 40q^{16} + 16q^{22} - 8q^{23} + 56q^{25} + 12q^{26} + 12q^{31} - 8q^{37} + 12q^{38} + 24q^{47} - 48q^{49} + 28q^{53} - 4q^{56} - 12q^{58} - 60q^{59} - 80q^{64} + 28q^{67} + 36q^{70} + 104q^{71} - 24q^{77} + 12q^{80} + 48q^{82} + 4q^{86} + 8q^{88} - 24q^{89} + 92q^{91} - 16q^{92} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1386, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1386.2.bk.a $$16$$ $$11.067$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-12$$ $$-6$$ $$q-\beta _{12}q^{2}+(1+\beta _{13})q^{4}+(-1-\beta _{9}+\cdots)q^{5}+\cdots$$
1386.2.bk.b $$16$$ $$11.067$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-12$$ $$6$$ $$q+\beta _{12}q^{2}+(1+\beta _{13})q^{4}+(-1-\beta _{9}+\cdots)q^{5}+\cdots$$
1386.2.bk.c $$16$$ $$11.067$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$12$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{10}q^{4}+(\beta _{8}+\beta _{10})q^{5}+\cdots$$
1386.2.bk.d $$32$$ $$11.067$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1386, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1386, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(154, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(462, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(693, [\chi])$$$$^{\oplus 2}$$