# Properties

 Label 1008.2.q Level $1008$ Weight $2$ Character orbit 1008.q Rep. character $\chi_{1008}(529,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $92$ Newform subspaces $12$ 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.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$12$$ 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 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

## Trace form

 $$92q + q^{3} + q^{5} + q^{7} - q^{9} + O(q^{10})$$ $$92q + q^{3} + q^{5} + q^{7} - q^{9} - q^{11} - 2q^{13} + 7q^{15} - 2q^{17} + 2q^{19} - 3q^{21} - q^{23} - 37q^{25} + 4q^{27} - 6q^{29} + 14q^{31} + 5q^{33} + 9q^{35} - 2q^{37} + 16q^{39} - 2q^{41} - 4q^{43} + 13q^{45} + 42q^{47} - q^{49} - 19q^{51} - 2q^{53} + 18q^{55} - 6q^{57} - 70q^{59} - 2q^{61} + 2q^{65} + 2q^{67} - 31q^{69} + 32q^{71} - 2q^{73} - 33q^{75} + 21q^{77} + 2q^{79} - q^{81} + 28q^{83} + 3q^{85} + 31q^{87} + 2q^{89} - 4q^{91} - 5q^{93} - 54q^{95} - 2q^{97} + 61q^{99} + O(q^{100})$$

## 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.q.a $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$4$$ $$q+(1-2\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots$$
1008.2.q.b $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-4$$ $$q+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots$$
1008.2.q.c $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-4$$ $$q+(1-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$$
1008.2.q.d $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$4$$ $$q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
1008.2.q.e $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$4$$ $$q+(1-2\zeta_{6})q^{3}+(3-3\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
1008.2.q.f $$2$$ $$8.049$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$-2$$ $$5$$ $$q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
1008.2.q.g $$6$$ $$8.049$$ 6.0.309123.1 None $$0$$ $$-2$$ $$1$$ $$-2$$ $$q+(\beta _{2}+\beta _{4})q^{3}+(1-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots$$
1008.2.q.h $$6$$ $$8.049$$ 6.0.309123.1 None $$0$$ $$2$$ $$-5$$ $$-4$$ $$q+(-\beta _{3}+\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+2\beta _{4}+\cdots)q^{5}+\cdots$$
1008.2.q.i $$10$$ $$8.049$$ 10.0.$$\cdots$$.1 None $$0$$ $$1$$ $$4$$ $$4$$ $$q+\beta _{8}q^{3}+(\beta _{1}+\beta _{2}+\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$$
1008.2.q.j $$14$$ $$8.049$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$-3$$ $$-2$$ $$-6$$ $$q-\beta _{3}q^{3}+\beta _{4}q^{5}+\beta _{12}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$$
1008.2.q.k $$22$$ $$8.049$$ None $$0$$ $$-2$$ $$3$$ $$5$$
1008.2.q.l $$22$$ $$8.049$$ None $$0$$ $$2$$ $$1$$ $$-5$$

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

$$S_{2}^{\mathrm{old}}(1008, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 2}$$