# Properties

 Label 1008.2.do Level 1008 Weight 2 Character orbit do Rep. character $$\chi_{1008}(205,\cdot)$$ 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.do (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

 $$752q + 2q^{2} - 2q^{3} + 2q^{4} - 4q^{5} - 8q^{6} - 16q^{8} + O(q^{10})$$ $$752q + 2q^{2} - 2q^{3} + 2q^{4} - 4q^{5} - 8q^{6} - 16q^{8} - 4q^{10} - 4q^{11} - 2q^{12} - 4q^{13} - 10q^{14} - 16q^{15} + 2q^{16} - 8q^{17} - 30q^{18} - 4q^{19} - 4q^{20} + 8q^{21} - 4q^{22} + 18q^{24} - 4q^{26} - 8q^{27} - 4q^{29} - 34q^{30} + 4q^{31} + 22q^{32} - 4q^{33} + 2q^{35} + 20q^{36} - 4q^{37} - 4q^{38} - 4q^{40} + 14q^{42} - 4q^{43} + 18q^{44} + 38q^{45} + 4q^{46} - 76q^{47} - 48q^{48} - 4q^{49} + 4q^{50} - 30q^{51} - 4q^{52} - 4q^{53} - 62q^{54} - 68q^{56} - 4q^{58} + 2q^{59} + 22q^{60} + 2q^{61} - 112q^{62} - 36q^{63} - 16q^{64} + 4q^{65} - 34q^{66} + 2q^{67} + 28q^{68} - 2q^{69} + 12q^{70} - 14q^{72} - 60q^{74} + 12q^{75} - 4q^{76} + 54q^{77} - 42q^{78} + 4q^{79} - 4q^{80} - 4q^{81} - 8q^{82} + 16q^{83} + 92q^{84} + 6q^{85} - 44q^{86} - 4q^{88} - 80q^{90} - 36q^{91} + 12q^{92} + 10q^{93} + 18q^{94} + 4q^{95} - 108q^{96} - 8q^{97} - 46q^{98} + 10q^{99} + O(q^{100})$$

## 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