# Properties

 Label 224.2.q Level $224$ Weight $2$ Character orbit 224.q Rep. character $\chi_{224}(47,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $1$ Sturm bound $64$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$224 = 2^{5} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 224.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$56$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$64$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(224, [\chi])$$.

Total New Old
Modular forms 80 20 60
Cusp forms 48 12 36
Eisenstein series 32 8 24

## Trace form

 $$12 q + 6 q^{3} + O(q^{10})$$ $$12 q + 6 q^{3} + 6 q^{11} - 6 q^{17} + 6 q^{19} - 6 q^{33} - 18 q^{35} - 12 q^{49} - 6 q^{51} - 36 q^{57} - 42 q^{59} - 12 q^{65} - 30 q^{67} + 18 q^{73} - 24 q^{75} + 6 q^{81} + 18 q^{89} + 72 q^{91} + 24 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(224, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
224.2.q.a $12$ $1.789$ 12.0.$$\cdots$$.2 None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{8}q^{3}+(-\beta _{4}-\beta _{7})q^{5}+(\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(224, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(224, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 3}$$