# Properties

 Label 672.2.bi Level $672$ Weight $2$ Character orbit 672.bi Rep. character $\chi_{672}(17,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $56$ Newform subspaces $3$ Sturm bound $256$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$672 = 2^{5} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 672.bi (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$168$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$256$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(672, [\chi])$$.

Total New Old
Modular forms 288 72 216
Cusp forms 224 56 168
Eisenstein series 64 16 48

## Trace form

 $$56 q + 8 q^{7} - 2 q^{9} + O(q^{10})$$ $$56 q + 8 q^{7} - 2 q^{9} + 20 q^{15} + 8 q^{25} + 12 q^{31} - 6 q^{33} + 8 q^{39} - 16 q^{49} + 4 q^{57} + 30 q^{63} - 36 q^{73} + 36 q^{79} + 6 q^{81} + 24 q^{87} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(672, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
672.2.bi.a $4$ $5.366$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-6})$$ $$0$$ $$-6$$ $$-6$$ $$2$$ $$q+(-1+\beta _{2})q^{3}+(-2+\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$$
672.2.bi.b $4$ $5.366$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-6})$$ $$0$$ $$6$$ $$6$$ $$2$$ $$q+(1-\beta _{2})q^{3}+(2+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots$$
672.2.bi.c $48$ $5.366$ None $$0$$ $$0$$ $$0$$ $$4$$

## Decomposition of $$S_{2}^{\mathrm{old}}(672, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(672, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 2}$$