# Properties

 Label 1386.2.g Level $1386$ Weight $2$ Character orbit 1386.g Rep. character $\chi_{1386}(881,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $2$ 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.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$576$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 304 32 272
Cusp forms 272 32 240
Eisenstein series 32 0 32

## Trace form

 $$32q - 32q^{4} - 8q^{7} + O(q^{10})$$ $$32q - 32q^{4} - 8q^{7} + 32q^{16} + 64q^{25} + 8q^{28} - 32q^{37} - 32q^{43} - 16q^{46} + 32q^{49} - 32q^{64} + 32q^{67} + 16q^{70} + 80q^{79} + 32q^{85} - 32q^{91} + O(q^{100})$$

## 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.g.a $$16$$ $$11.067$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{1}q^{2}-q^{4}-\beta _{4}q^{5}+\beta _{7}q^{7}-\beta _{1}q^{8}+\cdots$$
1386.2.g.b $$16$$ $$11.067$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}-q^{4}+\beta _{1}q^{5}-\beta _{10}q^{7}-\beta _{5}q^{8}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1386, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(462, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(693, [\chi])$$$$^{\oplus 2}$$