# Properties

 Label 1008.2.em Level 1008 Weight 2 Character orbit em Rep. character $$\chi_{1008}(293,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 752 Sturm bound 384

# Related objects

## Defining parameters

 Level: $$N$$ = $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1008.em (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$1008$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$384$$

## Dimensions

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

Total New Old
Modular forms 784 784 0
Cusp forms 752 752 0
Eisenstein series 32 32 0

## Trace form

 $$752q - 12q^{2} - 4q^{4} + O(q^{10})$$ $$752q - 12q^{2} - 4q^{4} - 12q^{11} - 6q^{14} - 16q^{15} - 4q^{16} + 20q^{18} + 2q^{21} - 4q^{22} - 24q^{28} - 12q^{29} + 4q^{30} - 12q^{32} - 4q^{36} - 16q^{37} + 48q^{42} - 4q^{43} - 4q^{49} - 12q^{50} + 8q^{51} - 48q^{56} - 4q^{58} + 24q^{60} - 36q^{63} - 16q^{64} - 24q^{65} - 4q^{67} - 16q^{70} - 16q^{72} - 96q^{74} - 6q^{77} - 76q^{78} - 8q^{79} - 16q^{81} - 138q^{84} - 24q^{85} + 48q^{86} - 4q^{88} + 20q^{91} - 12q^{92} - 20q^{93} - 24q^{95} + 28q^{99} + O(q^{100})$$

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

The newforms in this space have not yet been added to the LMFDB.

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database