# Properties

 Label 684.2.bk Level $684$ Weight $2$ Character orbit 684.bk Rep. character $\chi_{684}(449,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $1$ Sturm bound $240$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$684 = 2^{2} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 684.bk (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$240$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(684, [\chi])$$.

Total New Old
Modular forms 264 16 248
Cusp forms 216 16 200
Eisenstein series 48 0 48

## Trace form

 $$16q + O(q^{10})$$ $$16q - 12q^{19} + 4q^{25} - 4q^{43} + 20q^{55} + 12q^{61} + 36q^{67} + 44q^{73} - 12q^{79} + 56q^{85} - 60q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(684, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
684.2.bk.a $$16$$ $$5.462$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}-\beta _{10})q^{5}+(\beta _{7}+\beta _{8})q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(684, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(684, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(342, [\chi])$$$$^{\oplus 2}$$