# Properties

 Label 1386.2.c Level $1386$ Weight $2$ Character orbit 1386.c Rep. character $\chi_{1386}(197,\cdot)$ Character field $\Q$ Dimension $24$ 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.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$576$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$17$$

## Dimensions

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

Total New Old
Modular forms 304 24 280
Cusp forms 272 24 248
Eisenstein series 32 0 32

## Trace form

 $$24q + 24q^{4} + O(q^{10})$$ $$24q + 24q^{4} + 24q^{16} - 8q^{22} - 8q^{25} + 32q^{34} + 48q^{37} - 24q^{49} - 16q^{55} + 32q^{58} + 24q^{64} - 96q^{67} - 16q^{70} + 32q^{82} - 8q^{88} + 96q^{97} + O(q^{100})$$

## 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.c.a $$12$$ $$11.067$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$-12$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}+(\beta _{1}-\beta _{5})q^{5}-\beta _{1}q^{7}+\cdots$$
1386.2.c.b $$12$$ $$11.067$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$12$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}+(\beta _{1}-\beta _{5})q^{5}+\beta _{1}q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1386, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(66, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(99, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(198, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(462, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(693, [\chi])$$$$^{\oplus 2}$$