# Properties

 Label 448.2.p Level $448$ Weight $2$ Character orbit 448.p Rep. character $\chi_{448}(255,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $28$ Newform subspaces $5$ Sturm bound $128$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$448 = 2^{6} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 448.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$128$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(448, [\chi])$$.

Total New Old
Modular forms 152 36 116
Cusp forms 104 28 76
Eisenstein series 48 8 40

## Trace form

 $$28q + 6q^{5} - 12q^{9} + O(q^{10})$$ $$28q + 6q^{5} - 12q^{9} - 6q^{17} + 14q^{21} + 4q^{25} - 8q^{29} - 6q^{33} + 18q^{37} - 12q^{45} - 4q^{49} - 6q^{53} + 4q^{57} + 6q^{61} + 8q^{65} - 6q^{73} - 6q^{77} - 22q^{81} + 76q^{85} - 54q^{89} - 18q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(448, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
448.2.p.a $$2$$ $$3.577$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-3$$ $$-4$$ $$q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots$$
448.2.p.b $$2$$ $$3.577$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-3$$ $$4$$ $$q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
448.2.p.c $$4$$ $$3.577$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$0$$ $$6$$ $$0$$ $$q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots$$
448.2.p.d $$4$$ $$3.577$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$6$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(1+\zeta_{12}^{2})q^{5}+\cdots$$
448.2.p.e $$16$$ $$3.577$$ 16.0.$$\cdots$$.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{14}q^{3}+\beta _{13}q^{5}+\beta _{9}q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(448, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(448, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(224, [\chi])$$$$^{\oplus 2}$$