# Properties

 Label 896.2.u Level $896$ Weight $2$ Character orbit 896.u Rep. character $\chi_{896}(113,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $96$ Newform subspaces $3$ Sturm bound $256$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$896 = 2^{7} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 896.u (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$32$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$3$$ Sturm bound: $$256$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 544 96 448
Cusp forms 480 96 384
Eisenstein series 64 0 64

## Trace form

 $$96q + O(q^{10})$$ $$96q + 8q^{23} + 48q^{27} + 48q^{39} + 8q^{43} - 32q^{51} - 16q^{53} - 64q^{55} - 64q^{61} - 40q^{63} - 40q^{67} - 64q^{69} - 64q^{75} - 16q^{77} + 112q^{87} + 128q^{95} + 128q^{99} + O(q^{100})$$

## 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.u.a $$4$$ $$7.155$$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$-8$$ $$0$$ $$q+(1+\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2-2\zeta_{8}+\cdots)q^{5}+\cdots$$
896.2.u.b $$40$$ $$7.155$$ None $$0$$ $$-4$$ $$8$$ $$0$$
896.2.u.c $$52$$ $$7.155$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(896, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(224, [\chi])$$$$^{\oplus 3}$$