# Properties

 Label 1008.2.ch Level 1008 Weight 2 Character orbit ch Rep. character $$\chi_{1008}(239,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 72 Newform subspaces 3 Sturm bound 384 Trace bound 3

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## Defining parameters

 Level: $$N$$ = $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1008.ch (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$36$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$384$$ Trace bound: $$3$$

## Dimensions

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

Total New Old
Modular forms 408 72 336
Cusp forms 360 72 288
Eisenstein series 48 0 48

## Trace form

 $$72q - 12q^{9} + O(q^{10})$$ $$72q - 12q^{9} + 36q^{25} + 36q^{33} + 36q^{41} + 24q^{45} + 36q^{49} - 36q^{57} - 72q^{65} - 24q^{69} + 72q^{73} - 36q^{81} + 48q^{93} + 36q^{97} + O(q^{100})$$

## 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.ch.a $$24$$ $$8.049$$ None $$0$$ $$-6$$ $$6$$ $$0$$
1008.2.ch.b $$24$$ $$8.049$$ None $$0$$ $$0$$ $$-12$$ $$0$$
1008.2.ch.c $$24$$ $$8.049$$ None $$0$$ $$6$$ $$6$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(1008, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 3}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database