# Properties

 Label 1008.2.cz Level $1008$ Weight $2$ Character orbit 1008.cz Rep. character $\chi_{1008}(367,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $96$ Newform subspaces $9$ Sturm bound $384$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1008.cz (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$252$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$9$$ Sturm bound: $$384$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1008, [\chi])$$.

Total New Old
Modular forms 408 96 312
Cusp forms 360 96 264
Eisenstein series 48 0 48

## Trace form

 $$96q + O(q^{10})$$ $$96q + 12q^{21} + 48q^{25} - 12q^{29} + 36q^{45} - 24q^{57} - 48q^{65} - 24q^{77} + 48q^{81} + 36q^{89} - 24q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1008, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1008.2.cz.a $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$0$$ $$-1$$ $$q+(-2+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots$$
1008.2.cz.b $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$-4$$ $$q+(1-2\zeta_{6})q^{3}+(-1-\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots$$
1008.2.cz.c $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$4$$ $$q+(-1+2\zeta_{6})q^{3}+(-1-\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots$$
1008.2.cz.d $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$0$$ $$1$$ $$q+(2-\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots$$
1008.2.cz.e $$4$$ $$8.049$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$6$$ $$-4$$ $$q+(1+2\beta _{1})q^{3}+(2+\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots$$
1008.2.cz.f $$4$$ $$8.049$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$6$$ $$4$$ $$q+(-1-2\beta _{1})q^{3}+(2+\beta _{1}+\beta _{3})q^{5}+\cdots$$
1008.2.cz.g $$24$$ $$8.049$$ None $$0$$ $$-3$$ $$-3$$ $$4$$
1008.2.cz.h $$24$$ $$8.049$$ None $$0$$ $$3$$ $$-3$$ $$-4$$
1008.2.cz.i $$32$$ $$8.049$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1008, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1008, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 3}$$