# Properties

 Label 1512.2.cy Level 1512 Weight 2 Character orbit cy Rep. character $$\chi_{1512}(179,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 184 Sturm bound 576

# Related objects

## Defining parameters

 Level: $$N$$ = $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1512.cy (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$504$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$576$$

## Dimensions

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

Total New Old
Modular forms 600 200 400
Cusp forms 552 184 368
Eisenstein series 48 16 32

## Trace form

 $$184q + 3q^{2} + q^{4} + O(q^{10})$$ $$184q + 3q^{2} + q^{4} - 6q^{10} + 3q^{14} + q^{16} - 4q^{19} + 6q^{20} + 2q^{22} + 148q^{25} - 6q^{26} + 33q^{32} - 4q^{34} + 30q^{35} - 12q^{40} + 12q^{41} - 4q^{43} + 9q^{44} - 6q^{46} - 2q^{49} + 21q^{50} - 18q^{52} - 18q^{56} + 6q^{58} + 6q^{59} - 8q^{64} + 6q^{65} + 2q^{67} - 18q^{70} - 4q^{73} + 2q^{76} + 87q^{80} - 4q^{82} + 72q^{83} + 14q^{88} - 24q^{89} - 36q^{91} + 36q^{92} + 9q^{94} - 4q^{97} + 57q^{98} + O(q^{100})$$

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

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

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

$$S_{2}^{\mathrm{old}}(1512, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database