# Properties

 Label 1512.2.dx Level 1512 Weight 2 Character orbit dx Rep. character $$\chi_{1512}(85,\cdot)$$ Character field $$\Q(\zeta_{18})$$ Dimension 1296 Sturm bound 576

# Related objects

## Defining parameters

 Level: $$N$$ = $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1512.dx (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$216$$ 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 1296 456
Cusp forms 1704 1296 408
Eisenstein series 48 0 48

## Trace form

 $$1296q + O(q^{10})$$ $$1296q - 18q^{12} + 42q^{18} - 42q^{20} + 36q^{26} + 48q^{30} + 30q^{32} - 24q^{33} + 24q^{41} + 30q^{42} - 48q^{44} + 18q^{48} + 156q^{50} + 54q^{52} - 54q^{58} - 186q^{60} + 6q^{66} - 78q^{68} + 168q^{71} - 42q^{72} - 180q^{80} - 30q^{86} + 72q^{87} + 30q^{90} - 114q^{92} + 54q^{94} - 156q^{96} + O(q^{100})$$

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

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1512, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1512, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(216, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database