# Properties

 Label 3024.2.hc Level 3024 Weight 2 Character orbit hc Rep. character $$\chi_{3024}(347,\cdot)$$ Character field $$\Q(\zeta_{36})$$ Dimension 6864 Sturm bound 1152

# Related objects

## Defining parameters

 Level: $$N$$ = $$3024 = 2^{4} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3024.hc (of order $$36$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$3024$$ Character field: $$\Q(\zeta_{36})$$ Sturm bound: $$1152$$

## Dimensions

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

Total New Old
Modular forms 6960 6960 0
Cusp forms 6864 6864 0
Eisenstein series 96 96 0

## Trace form

 $$6864q - 6q^{2} - 6q^{3} - 6q^{4} - 6q^{5} - 24q^{6} - 24q^{7} - 36q^{8} + O(q^{10})$$ $$6864q - 6q^{2} - 6q^{3} - 6q^{4} - 6q^{5} - 24q^{6} - 24q^{7} - 36q^{8} + 6q^{10} - 6q^{11} - 6q^{12} - 24q^{13} - 12q^{14} - 6q^{16} - 36q^{17} - 6q^{18} + 6q^{19} - 24q^{20} - 12q^{21} - 24q^{22} - 12q^{23} + 114q^{24} - 24q^{27} - 24q^{28} - 24q^{29} - 6q^{30} - 6q^{32} - 12q^{33} - 12q^{34} - 18q^{35} - 24q^{36} - 12q^{37} - 6q^{38} - 12q^{39} - 6q^{40} - 42q^{42} - 24q^{43} - 6q^{45} - 12q^{46} - 24q^{48} - 24q^{49} - 24q^{50} - 42q^{51} - 6q^{52} - 90q^{54} - 96q^{55} - 54q^{56} - 6q^{58} - 6q^{59} + 114q^{60} - 6q^{61} + 162q^{62} - 12q^{64} - 12q^{65} - 6q^{66} - 6q^{67} - 54q^{68} - 24q^{69} + 30q^{70} - 72q^{71} + 6q^{72} - 90q^{74} - 6q^{75} - 24q^{76} - 12q^{77} - 24q^{78} - 12q^{81} - 12q^{82} + 36q^{83} - 192q^{84} + 6q^{85} + 114q^{86} - 12q^{87} - 6q^{88} + 30q^{90} - 6q^{91} - 24q^{92} - 6q^{93} - 6q^{94} - 438q^{96} - 48q^{97} - 18q^{98} - 24q^{99} + O(q^{100})$$

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

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

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database