# Properties

 Label 1512.2.ew Level 1512 Weight 2 Character orbit ew Rep. character $$\chi_{1512}(5,\cdot)$$ Character field $$\Q(\zeta_{18})$$ Dimension 1704 Sturm bound 576

# Related objects

## Defining parameters

 Level: $$N$$ = $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1512.ew (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$1512$$ Character field: $$\Q(\zeta_{18})$$ Sturm bound: $$576$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1512, [\chi])$$.

Total New Old
Modular forms 1752 1752 0
Cusp forms 1704 1704 0
Eisenstein series 48 48 0

## Trace form

 $$1704q - 3q^{2} - 3q^{4} - 12q^{7} - 18q^{8} - 6q^{9} + O(q^{10})$$ $$1704q - 3q^{2} - 3q^{4} - 12q^{7} - 18q^{8} - 6q^{9} - 9q^{12} - 21q^{14} - 24q^{15} - 3q^{16} - 36q^{17} - 3q^{18} - 12q^{22} - 6q^{23} - 9q^{24} - 6q^{25} - 12q^{28} - 39q^{30} - 18q^{31} - 33q^{32} - 18q^{33} - 18q^{34} - 42q^{36} + 81q^{38} - 6q^{39} + 36q^{40} - 21q^{42} - 9q^{44} + 3q^{46} - 18q^{47} - 12q^{49} - 27q^{50} - 9q^{52} + 117q^{54} + 15q^{56} - 42q^{57} - 3q^{58} - 33q^{60} - 99q^{62} + 48q^{63} - 6q^{64} - 6q^{65} - 9q^{66} - 54q^{68} + 24q^{70} - 36q^{71} - 63q^{72} - 18q^{73} + 69q^{74} - 36q^{76} - 30q^{78} - 6q^{79} - 6q^{81} - 18q^{82} - 144q^{84} + 135q^{86} - 18q^{87} + 45q^{88} - 36q^{89} + 81q^{90} - 72q^{92} - 9q^{94} - 126q^{95} - 9q^{96} - 9q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1512, [\chi])$$ 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