# Properties

 Label 1008.2.dx Level 1008 Weight 2 Character orbit dx Rep. character $$\chi_{1008}(277,\cdot)$$ 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.dx (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

 $$752q - 4q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 8q^{6} - 16q^{8} + O(q^{10})$$ $$752q - 4q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 8q^{6} - 16q^{8} - 4q^{10} + 2q^{11} - 2q^{12} - 4q^{13} + 14q^{14} - 16q^{15} - 4q^{16} - 8q^{17} + 24q^{18} - 4q^{19} - 4q^{20} - 10q^{21} - 4q^{22} + 18q^{24} - 4q^{26} - 8q^{27} - 4q^{29} + 14q^{30} - 8q^{31} - 44q^{32} - 4q^{33} + 2q^{35} + 20q^{36} - 4q^{37} + 2q^{38} + 2q^{40} - 46q^{42} - 4q^{43} + 18q^{44} - 22q^{45} + 4q^{46} + 152q^{47} - 48q^{48} - 4q^{49} + 4q^{50} + 30q^{51} + 2q^{52} - 4q^{53} + 70q^{54} + 52q^{56} + 2q^{58} - 4q^{59} - 86q^{60} - 4q^{61} - 112q^{62} + 48q^{63} - 16q^{64} - 8q^{65} + 2q^{66} - 4q^{67} - 14q^{68} - 2q^{69} - 30q^{70} - 14q^{72} + 30q^{74} + 6q^{75} - 4q^{76} - 30q^{77} - 42q^{78} - 8q^{79} - 4q^{80} - 4q^{81} - 8q^{82} + 16q^{83} + 50q^{84} + 6q^{85} + 22q^{86} + 2q^{88} - 80q^{90} - 36q^{91} + 12q^{92} - 26q^{93} - 36q^{94} - 8q^{95} - 6q^{96} - 8q^{97} - 46q^{98} + 10q^{99} + O(q^{100})$$

## 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