# Properties

 Label 3024.2.en Level 3024 Weight 2 Character orbit en Rep. character $$\chi_{3024}(19,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 752 Sturm bound 1152

# Related objects

## Defining parameters

 Level: $$N$$ = $$3024 = 2^{4} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3024.en (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$1008$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$1152$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3024, [\chi])$$.

Total New Old
Modular forms 2352 784 1568
Cusp forms 2256 752 1504
Eisenstein series 96 32 64

## Trace form

 $$752q - 2q^{2} + 2q^{4} - 4q^{7} + 16q^{8} + O(q^{10})$$ $$752q - 2q^{2} + 2q^{4} - 4q^{7} + 16q^{8} - 12q^{10} + 4q^{11} - 6q^{14} + 2q^{16} + 24q^{17} - 12q^{19} - 4q^{22} + 8q^{23} + 12q^{26} - 16q^{28} + 4q^{29} + 18q^{32} + 12q^{34} - 2q^{35} - 4q^{37} - 4q^{43} + 26q^{44} - 12q^{46} - 4q^{49} - 4q^{50} + 4q^{53} + 96q^{56} - 4q^{58} + 6q^{59} - 6q^{61} - 16q^{64} - 4q^{65} + 2q^{67} + 12q^{70} + 32q^{71} - 52q^{74} + 58q^{77} + 12q^{80} + 60q^{83} - 14q^{85} + 44q^{86} - 4q^{88} - 36q^{91} + 20q^{92} - 6q^{94} - 22q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3024, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(3024, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3024, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(1008, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database