# Properties

 Label 448.2.q Level $448$ Weight $2$ Character orbit 448.q Rep. character $\chi_{448}(31,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $32$ Newform subspaces $3$ Sturm bound $128$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$448 = 2^{6} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 448.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$56$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$128$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$5$$

## Dimensions

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

Total New Old
Modular forms 152 32 120
Cusp forms 104 32 72
Eisenstein series 48 0 48

## Trace form

 $$32q + 16q^{9} + O(q^{10})$$ $$32q + 16q^{9} - 16q^{25} + 16q^{49} + 32q^{57} - 48q^{73} + 32q^{81} - 144q^{89} + O(q^{100})$$

## 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.q.a $$8$$ $$3.577$$ 8.0.12960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}+\beta _{7})q^{3}+\beta _{6}q^{5}+(2\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots$$
448.2.q.b $$12$$ $$3.577$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$-6$$ $$0$$ $$q-\beta _{5}q^{3}+(\beta _{6}-\beta _{7})q^{5}+(\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots$$
448.2.q.c $$12$$ $$3.577$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$6$$ $$0$$ $$q-\beta _{5}q^{3}+(-\beta _{6}+\beta _{7})q^{5}+(-\beta _{4}+\beta _{10}+\cdots)q^{7}+\cdots$$

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

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