# Properties

 Label 1512.2.dv Level 1512 Weight 2 Character orbit dv Rep. character $$\chi_{1512}(41,\cdot)$$ Character field $$\Q(\zeta_{18})$$ Dimension 432 Sturm bound 576

# Related objects

## Defining parameters

 Level: $$N$$ = $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1512.dv (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$189$$ 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 1776 432 1344
Cusp forms 1680 432 1248
Eisenstein series 96 0 96

## Trace form

 $$432q + O(q^{10})$$ $$432q - 12q^{15} + 12q^{21} - 12q^{23} + 36q^{29} - 36q^{39} - 18q^{49} + 36q^{63} - 36q^{65} + 60q^{77} + 36q^{81} - 72q^{93} - 216q^{95} + 216q^{99} + O(q^{100})$$

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

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

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

$$S_{2}^{\mathrm{old}}(1512, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(378, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(756, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database