# Properties

 Label 896.2.b Level $896$ Weight $2$ Character orbit 896.b Rep. character $\chi_{896}(449,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $8$ Sturm bound $256$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$896 = 2^{7} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 896.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$256$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$, $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(896, [\chi])$$.

Total New Old
Modular forms 144 24 120
Cusp forms 112 24 88
Eisenstein series 32 0 32

## Trace form

 $$24q - 24q^{9} + O(q^{10})$$ $$24q - 24q^{9} - 16q^{17} - 8q^{25} + 32q^{33} - 16q^{41} + 24q^{49} - 32q^{57} - 64q^{65} + 48q^{73} + 56q^{81} + 48q^{89} - 16q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(896, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
896.2.b.a $$2$$ $$7.155$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}-iq^{5}-q^{7}-q^{9}-iq^{13}+\cdots$$
896.2.b.b $$2$$ $$7.155$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+\beta q^{5}-q^{7}+3q^{9}-\beta q^{11}+\beta q^{13}+\cdots$$
896.2.b.c $$2$$ $$7.155$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+iq^{5}+q^{7}-q^{9}+iq^{13}+\cdots$$
896.2.b.d $$2$$ $$7.155$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+\beta q^{5}+q^{7}+3q^{9}+\beta q^{11}+\beta q^{13}+\cdots$$
896.2.b.e $$4$$ $$7.155$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{3}+\beta _{1}q^{5}-q^{7}+(-3+\beta _{3})q^{9}+\cdots$$
896.2.b.f $$4$$ $$7.155$$ 4.0.2048.2 None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{3}-\beta _{1}q^{5}-q^{7}+(-1-\beta _{3})q^{9}+\cdots$$
896.2.b.g $$4$$ $$7.155$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{3}-\beta _{1}q^{5}+q^{7}+(-3+\beta _{3})q^{9}+\cdots$$
896.2.b.h $$4$$ $$7.155$$ 4.0.2048.2 None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(-1-\beta _{3})q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(896, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(896, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(224, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(448, [\chi])$$$$^{\oplus 2}$$