# Properties

 Label 1386.2.ba Level $1386$ Weight $2$ Character orbit 1386.ba Rep. character $\chi_{1386}(989,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $64$ Newform subspaces $2$ Sturm bound $576$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.ba (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$231$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$576$$ Trace bound: $$2$$

## Dimensions

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

Total New Old
Modular forms 608 64 544
Cusp forms 544 64 480
Eisenstein series 64 0 64

## Trace form

 $$64q - 32q^{4} + O(q^{10})$$ $$64q - 32q^{4} - 32q^{16} + 8q^{22} + 8q^{25} + 8q^{31} + 16q^{34} + 8q^{37} + 40q^{49} - 24q^{55} + 16q^{58} + 64q^{64} - 16q^{67} - 8q^{70} - 32q^{82} - 4q^{88} - 64q^{97} + O(q^{100})$$

## 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.ba.a $$32$$ $$11.067$$ None $$-16$$ $$0$$ $$0$$ $$0$$
1386.2.ba.b $$32$$ $$11.067$$ None $$16$$ $$0$$ $$0$$ $$0$$

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

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