# Properties

 Label 1008.2.ef Level 1008 Weight 2 Character orbit ef Rep. character $$\chi_{1008}(115,\cdot)$$ 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.ef (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

 $$752q - 4q^{2} - 6q^{3} - 4q^{4} - 6q^{5} - 4q^{7} - 16q^{8} + O(q^{10})$$ $$752q - 4q^{2} - 6q^{3} - 4q^{4} - 6q^{5} - 4q^{7} - 16q^{8} - 12q^{10} + 2q^{11} - 6q^{12} - 18q^{14} - 4q^{16} - 24q^{17} + 4q^{18} - 12q^{19} - 10q^{21} - 4q^{22} + 4q^{23} - 6q^{24} - 12q^{26} - 16q^{28} - 4q^{29} - 18q^{30} + 36q^{32} - 12q^{33} - 12q^{34} + 2q^{35} - 20q^{36} - 4q^{37} - 6q^{38} - 4q^{39} - 6q^{40} - 46q^{42} - 4q^{43} - 26q^{44} - 6q^{45} - 12q^{46} - 4q^{49} + 4q^{50} - 34q^{51} - 6q^{52} - 4q^{53} + 78q^{54} + 24q^{56} + 2q^{58} - 30q^{60} - 16q^{64} - 8q^{65} - 66q^{66} - 4q^{67} - 6q^{68} + 18q^{69} - 30q^{70} - 32q^{71} - 14q^{72} - 26q^{74} - 6q^{75} + 26q^{77} - 50q^{78} - 12q^{80} - 4q^{81} + 60q^{83} - 2q^{84} - 14q^{85} + 22q^{86} - 12q^{87} + 2q^{88} - 108q^{90} - 36q^{91} - 20q^{92} - 26q^{93} - 6q^{96} + 22q^{98} + 10q^{99} + O(q^{100})$$

## 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