# Properties

 Label 672.2.q Level $672$ Weight $2$ Character orbit 672.q Rep. character $\chi_{672}(193,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $32$ Newform subspaces $12$ Sturm bound $256$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$672 = 2^{5} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 672.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$12$$ Sturm bound: $$256$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 288 32 256
Cusp forms 224 32 192
Eisenstein series 64 0 64

## Trace form

 $$32 q - 16 q^{9} + O(q^{10})$$ $$32 q - 16 q^{9} + 16 q^{13} - 16 q^{21} - 8 q^{25} + 8 q^{33} - 8 q^{37} - 32 q^{41} + 32 q^{49} + 16 q^{53} + 16 q^{57} + 32 q^{61} + 16 q^{65} - 24 q^{73} + 32 q^{77} - 16 q^{81} + 128 q^{85} - 32 q^{89} - 24 q^{93} + 16 q^{97} + O(q^{100})$$

## 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.q.a $2$ $5.366$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-3$$ $$1$$ $$q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$$
672.2.q.b $2$ $5.366$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-1$$ $$-5$$ $$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots$$
672.2.q.c $2$ $5.366$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$1$$ $$q+(-1+\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$$
672.2.q.d $2$ $5.366$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$5$$ $$q+(-1+\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$$
672.2.q.e $2$ $5.366$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$4$$ $$5$$ $$q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
672.2.q.f $2$ $5.366$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-3$$ $$-1$$ $$q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$$
672.2.q.g $2$ $5.366$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-1$$ $$5$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots$$
672.2.q.h $2$ $5.366$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$-5$$ $$q+(1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$$
672.2.q.i $2$ $5.366$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$-1$$ $$q+(1-\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$$
672.2.q.j $2$ $5.366$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$4$$ $$-5$$ $$q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
672.2.q.k $6$ $5.366$ 6.0.1156923.1 None $$0$$ $$-3$$ $$0$$ $$-3$$ $$q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$$
672.2.q.l $6$ $5.366$ 6.0.1156923.1 None $$0$$ $$3$$ $$0$$ $$3$$ $$q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(672, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(224, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 2}$$