# Properties

 Label 1008.2.dk Level 1008 Weight 2 Character orbit dk Rep. character $$\chi_{1008}(139,\cdot)$$ 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.dk (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

 $$752q - 4q^{2} - 4q^{4} - 4q^{7} - 16q^{8} + O(q^{10})$$ $$752q - 4q^{2} - 4q^{4} - 4q^{7} - 16q^{8} - 4q^{11} + 6q^{14} - 4q^{16} + 4q^{18} - 10q^{21} - 4q^{22} - 8q^{23} + 8q^{28} - 4q^{29} - 36q^{30} + 36q^{32} - 28q^{35} - 44q^{36} - 16q^{37} - 16q^{39} - 16q^{42} - 4q^{43} - 104q^{44} - 4q^{49} - 20q^{50} + 56q^{51} - 16q^{53} + 24q^{56} - 4q^{58} - 120q^{60} - 16q^{64} - 8q^{65} - 4q^{67} + 12q^{70} - 32q^{71} + 112q^{72} - 32q^{74} + 26q^{77} + 76q^{78} - 16q^{81} - 14q^{84} + 16q^{85} + 16q^{86} - 4q^{88} - 36q^{91} + 28q^{92} + 4q^{93} - 68q^{98} - 44q^{99} + O(q^{100})$$

## 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