# Properties

 Label 1512.2.ca Level 1512 Weight 2 Character orbit ca Rep. character $$\chi_{1512}(341,\cdot)$$ 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.ca (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

 $$184q - 2q^{4} - 2q^{7} + O(q^{10})$$ $$184q - 2q^{4} - 2q^{7} - 6q^{10} + 18q^{14} - 2q^{16} - 6q^{22} + 6q^{23} + 78q^{25} + 6q^{26} - 8q^{28} + 6q^{34} + 33q^{38} - 18q^{40} + 9q^{44} + 2q^{46} + 12q^{47} - 2q^{49} - 9q^{50} + 21q^{52} - 18q^{56} - 3q^{58} - 12q^{62} - 8q^{64} + 18q^{68} - 27q^{70} - 12q^{73} + 57q^{74} + 12q^{76} - 4q^{79} + 57q^{80} + 27q^{86} + 9q^{88} + 24q^{89} + 36q^{92} + 45q^{98} + O(q^{100})$$

## 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