# Properties

 Label 1512.2.en Level 1512 Weight 2 Character orbit en Rep. character $$\chi_{1512}(139,\cdot)$$ 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.en (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

 $$1704q - 12q^{2} - 12q^{4} - 6q^{8} - 24q^{9} + O(q^{10})$$ $$1704q - 12q^{2} - 12q^{4} - 6q^{8} - 24q^{9} - 24q^{11} + 9q^{14} - 12q^{16} - 12q^{18} - 12q^{22} - 24q^{25} - 12q^{28} - 30q^{30} - 42q^{32} - 6q^{35} + 48q^{36} - 36q^{42} - 24q^{43} - 6q^{44} - 6q^{46} - 12q^{49} + 18q^{50} - 60q^{51} + 57q^{56} - 60q^{57} - 12q^{58} - 42q^{60} - 6q^{64} - 24q^{65} - 24q^{67} + 21q^{70} + 78q^{72} - 66q^{74} + 24q^{78} - 24q^{81} - 78q^{84} - 90q^{86} + 36q^{88} - 6q^{91} + 108q^{92} - 60q^{98} - 24q^{99} + O(q^{100})$$

## 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