# Properties

 Label 1386.2.e Level $1386$ Weight $2$ Character orbit 1386.e Rep. character $\chi_{1386}(307,\cdot)$ Character field $\Q$ Dimension $40$ Newform subspaces $5$ Sturm bound $576$ Trace bound $22$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$576$$ Trace bound: $$22$$ 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 304 40 264
Cusp forms 272 40 232
Eisenstein series 32 0 32

## Trace form

 $$40q - 40q^{4} + O(q^{10})$$ $$40q - 40q^{4} + 12q^{11} + 8q^{14} + 40q^{16} - 4q^{22} - 16q^{23} - 32q^{25} - 40q^{37} - 12q^{44} - 24q^{49} + 56q^{53} - 8q^{56} - 24q^{58} - 40q^{64} + 8q^{67} + 24q^{70} - 32q^{71} + 12q^{77} + 32q^{86} + 4q^{88} + 40q^{91} + 16q^{92} + O(q^{100})$$

## 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.e.a $$8$$ $$11.067$$ 8.0.6679465984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
1386.2.e.b $$8$$ $$11.067$$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$$
1386.2.e.c $$8$$ $$11.067$$ 8.0.157351936.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-q^{4}-\beta _{5}q^{5}+\beta _{1}q^{7}-\beta _{2}q^{8}+\cdots$$
1386.2.e.d $$8$$ $$11.067$$ 8.0.40960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-q^{4}-\beta _{4}q^{5}+(\beta _{2}-\beta _{7})q^{7}+\cdots$$
1386.2.e.e $$8$$ $$11.067$$ 8.0.6679465984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots$$

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

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