# Properties

 Label 1344.2.k Level $1344$ Weight $2$ Character orbit 1344.k Rep. character $\chi_{1344}(1217,\cdot)$ Character field $\Q$ Dimension $60$ Newform subspaces $10$ Sturm bound $512$ Trace bound $15$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1344 = 2^{6} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1344.k (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$512$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$5$$, $$43$$

## Dimensions

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

Total New Old
Modular forms 280 68 212
Cusp forms 232 60 172
Eisenstein series 48 8 40

## Trace form

 $$60q - 4q^{9} + O(q^{10})$$ $$60q - 4q^{9} - 4q^{21} + 36q^{25} + 24q^{37} - 4q^{49} + 8q^{57} + 28q^{81} + 48q^{85} - 8q^{93} + O(q^{100})$$

## 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.k.a $$2$$ $$10.732$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\zeta_{6}q^{3}+(-2-\zeta_{6})q^{7}-3q^{9}+4\zeta_{6}q^{13}+\cdots$$
1344.2.k.b $$2$$ $$10.732$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{6}q^{3}+(2-\zeta_{6})q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots$$
1344.2.k.c $$4$$ $$10.732$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$$
1344.2.k.d $$4$$ $$10.732$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots$$
1344.2.k.e $$8$$ $$10.732$$ 8.0.342102016.5 None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots$$
1344.2.k.f $$8$$ $$10.732$$ 8.0.342102016.5 None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-1-\beta _{5})q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots$$
1344.2.k.g $$8$$ $$10.732$$ 8.0.49787136.1 $$\Q(\sqrt{-21})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{5}q^{5}+\beta _{2}q^{7}-3q^{9}+\beta _{3}q^{11}+\cdots$$
1344.2.k.h $$8$$ $$10.732$$ 8.0.40960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{4}+\beta _{5})q^{3}+\beta _{7}q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$$
1344.2.k.i $$8$$ $$10.732$$ 8.0.342102016.5 None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{4}q^{3}-\beta _{2}q^{5}+(1+\beta _{5}+\beta _{6}+\beta _{7})q^{7}+\cdots$$
1344.2.k.j $$8$$ $$10.732$$ 8.0.342102016.5 None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{3}q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1344, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(672, [\chi])$$$$^{\oplus 2}$$