# Properties

 Label 1344.4.b Level $1344$ Weight $4$ Character orbit 1344.b Rep. character $\chi_{1344}(895,\cdot)$ Character field $\Q$ Dimension $96$ Newform subspaces $10$ Sturm bound $1024$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1344 = 2^{6} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1344.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$1024$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(1344, [\chi])$$.

Total New Old
Modular forms 792 96 696
Cusp forms 744 96 648
Eisenstein series 48 0 48

## Trace form

 $$96q + 864q^{9} + O(q^{10})$$ $$96q + 864q^{9} - 120q^{21} - 2400q^{25} - 400q^{29} - 1024q^{37} - 752q^{53} + 3504q^{77} + 7776q^{81} - 4704q^{85} + 3696q^{93} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(1344, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1344.4.b.a $$2$$ $$79.299$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-6$$ $$0$$ $$-28$$ $$q-3q^{3}-8\zeta_{6}q^{5}+(-14-7\zeta_{6})q^{7}+\cdots$$
1344.4.b.b $$2$$ $$79.299$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$-6$$ $$0$$ $$34$$ $$q-3q^{3}+\beta q^{5}+(17-3\beta )q^{7}+9q^{9}+\cdots$$
1344.4.b.c $$2$$ $$79.299$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$6$$ $$0$$ $$-34$$ $$q+3q^{3}+\beta q^{5}+(-17+3\beta )q^{7}+9q^{9}+\cdots$$
1344.4.b.d $$2$$ $$79.299$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$6$$ $$0$$ $$28$$ $$q+3q^{3}-8\zeta_{6}q^{5}+(14+7\zeta_{6})q^{7}+9q^{9}+\cdots$$
1344.4.b.e $$8$$ $$79.299$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$-24$$ $$0$$ $$4$$ $$q-3q^{3}+\beta _{5}q^{5}-\beta _{3}q^{7}+9q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$$
1344.4.b.f $$8$$ $$79.299$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$24$$ $$0$$ $$-4$$ $$q+3q^{3}+\beta _{5}q^{5}+\beta _{3}q^{7}+9q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$$
1344.4.b.g $$12$$ $$79.299$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-36$$ $$0$$ $$-10$$ $$q-3q^{3}-\beta _{7}q^{5}+(-1-\beta _{2})q^{7}+9q^{9}+\cdots$$
1344.4.b.h $$12$$ $$79.299$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$36$$ $$0$$ $$10$$ $$q+3q^{3}-\beta _{7}q^{5}+(1+\beta _{2})q^{7}+9q^{9}+\cdots$$
1344.4.b.i $$24$$ $$79.299$$ None $$0$$ $$-72$$ $$0$$ $$20$$
1344.4.b.j $$24$$ $$79.299$$ None $$0$$ $$72$$ $$0$$ $$-20$$

## Decomposition of $$S_{4}^{\mathrm{old}}(1344, [\chi])$$ into lower level spaces

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