# Properties

 Label 1008.3.cg Level $1008$ Weight $3$ Character orbit 1008.cg Rep. character $\chi_{1008}(145,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $78$ Newform subspaces $17$ Sturm bound $576$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1008.cg (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$17$$ Sturm bound: $$576$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1008, [\chi])$$.

Total New Old
Modular forms 816 82 734
Cusp forms 720 78 642
Eisenstein series 96 4 92

## Trace form

 $$78q + 3q^{5} - 6q^{7} + O(q^{10})$$ $$78q + 3q^{5} - 6q^{7} - 9q^{11} + 3q^{17} - 45q^{19} + 7q^{23} + 182q^{25} + 36q^{29} - 45q^{31} - 147q^{35} - 25q^{37} - 108q^{43} - 147q^{47} - 98q^{49} - 47q^{53} + 93q^{59} + 69q^{61} - 32q^{65} + 33q^{67} - 100q^{71} - 123q^{73} + 89q^{77} - 71q^{79} - 86q^{85} + 75q^{89} + 336q^{91} + 117q^{95} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(1008, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1008.3.cg.a $$2$$ $$27.466$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-9$$ $$-13$$ $$q+(-6+3\zeta_{6})q^{5}+(-5-3\zeta_{6})q^{7}+\cdots$$
1008.3.cg.b $$2$$ $$27.466$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$-13$$ $$q+(-2+\zeta_{6})q^{5}+(-5-3\zeta_{6})q^{7}+(3+\cdots)q^{11}+\cdots$$
1008.3.cg.c $$2$$ $$27.466$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$14$$ $$q+(-2+\zeta_{6})q^{5}+7q^{7}+(-15+15\zeta_{6})q^{11}+\cdots$$
1008.3.cg.d $$2$$ $$27.466$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-13$$ $$q+(-8+3\zeta_{6})q^{7}+(-7+14\zeta_{6})q^{13}+\cdots$$
1008.3.cg.e $$2$$ $$27.466$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$11$$ $$q+(8-5\zeta_{6})q^{7}+(-15+30\zeta_{6})q^{13}+\cdots$$
1008.3.cg.f $$2$$ $$27.466$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$6$$ $$7$$ $$q+(4-2\zeta_{6})q^{5}+7\zeta_{6}q^{7}+(-10+10\zeta_{6})q^{11}+\cdots$$
1008.3.cg.g $$2$$ $$27.466$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$9$$ $$7$$ $$q+(6-3\zeta_{6})q^{5}+(7-7\zeta_{6})q^{7}+(11-11\zeta_{6})q^{11}+\cdots$$
1008.3.cg.h $$4$$ $$27.466$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$-12$$ $$10$$ $$q+(-4-2\beta _{1}+\beta _{3})q^{5}+(-5\beta _{1}-\beta _{3})q^{7}+\cdots$$
1008.3.cg.i $$4$$ $$27.466$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-14$$ $$q+\beta _{3}q^{5}+7\beta _{1}q^{7}+(-2\beta _{2}-2\beta _{3})q^{11}+\cdots$$
1008.3.cg.j $$4$$ $$27.466$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$-14$$ $$q+\beta _{2}q^{5}+(-7-7\beta _{1})q^{7}+(2\beta _{2}-\beta _{3})q^{11}+\cdots$$
1008.3.cg.k $$4$$ $$27.466$$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$26$$ $$q+(-\beta _{2}+\beta _{3})q^{5}+(8-3\beta _{1})q^{7}+\beta _{2}q^{11}+\cdots$$
1008.3.cg.l $$4$$ $$27.466$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$6$$ $$-8$$ $$q+(2+\beta _{1}+2\beta _{3})q^{5}+(-1+2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
1008.3.cg.m $$4$$ $$27.466$$ $$\Q(\sqrt{-3}, \sqrt{65})$$ None $$0$$ $$0$$ $$9$$ $$-2$$ $$q+(2+\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{2})q^{7}+\cdots$$
1008.3.cg.n $$8$$ $$27.466$$ 8.0.$$\cdots$$.2 None $$0$$ $$0$$ $$-6$$ $$4$$ $$q+(-1-\beta _{4})q^{5}+(-\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$$
1008.3.cg.o $$8$$ $$27.466$$ 8.0.$$\cdots$$.2 None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{5}q^{5}+(2-\beta _{1}-3\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$$
1008.3.cg.p $$8$$ $$27.466$$ 8.0.$$\cdots$$.9 None $$0$$ $$0$$ $$6$$ $$-8$$ $$q+(1-\beta _{1}+\beta _{6})q^{5}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
1008.3.cg.q $$16$$ $$27.466$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{7}q^{5}+(-1+\beta _{2}-\beta _{5})q^{7}+(\beta _{4}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(1008, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1008, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(14, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 2}$$