# Properties

 Label 1344.2.bl Level $1344$ Weight $2$ Character orbit 1344.bl Rep. character $\chi_{1344}(703,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $64$ Newform subspaces $12$ Sturm bound $512$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1344 = 2^{6} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1344.bl (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$12$$ Sturm bound: $$512$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1344, [\chi])$$.

Total New Old
Modular forms 560 64 496
Cusp forms 464 64 400
Eisenstein series 96 0 96

## Trace form

 $$64q - 32q^{9} + O(q^{10})$$ $$64q - 32q^{9} - 16q^{21} + 32q^{25} + 32q^{29} - 24q^{37} + 16q^{53} + 48q^{77} - 32q^{81} - 96q^{85} + 8q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1344, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1344.2.bl.a $$2$$ $$10.732$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-6$$ $$-1$$ $$q+(-1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots$$
1344.2.bl.b $$2$$ $$10.732$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-3$$ $$-1$$ $$q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots$$
1344.2.bl.c $$2$$ $$10.732$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$3$$ $$5$$ $$q+(-1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}+\cdots$$
1344.2.bl.d $$2$$ $$10.732$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$6$$ $$-1$$ $$q+(-1+\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots$$
1344.2.bl.e $$2$$ $$10.732$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-6$$ $$1$$ $$q+(1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots$$
1344.2.bl.f $$2$$ $$10.732$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-3$$ $$1$$ $$q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots$$
1344.2.bl.g $$2$$ $$10.732$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$3$$ $$-5$$ $$q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-3+\zeta_{6})q^{7}+\cdots$$
1344.2.bl.h $$2$$ $$10.732$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$6$$ $$1$$ $$q+(1-\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots$$
1344.2.bl.i $$8$$ $$10.732$$ 8.0.562828176.1 None $$0$$ $$-4$$ $$0$$ $$-2$$ $$q+(-1+\beta _{1})q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
1344.2.bl.j $$8$$ $$10.732$$ 8.0.562828176.1 None $$0$$ $$4$$ $$0$$ $$2$$ $$q+(1-\beta _{1})q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$$
1344.2.bl.k $$16$$ $$10.732$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$-8$$ $$0$$ $$4$$ $$q+(-1+\beta _{1})q^{3}-\beta _{7}q^{5}+(\beta _{1}+\beta _{6}+\cdots)q^{7}+\cdots$$
1344.2.bl.l $$16$$ $$10.732$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$8$$ $$0$$ $$-4$$ $$q+(1-\beta _{1})q^{3}-\beta _{7}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1344, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1344, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(224, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(448, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(672, [\chi])$$$$^{\oplus 2}$$