# Properties

 Label 4008.2.bc Level 4008 Weight 2 Character orbit bc Rep. character $$\chi_{4008}(47,\cdot)$$ Character field $$\Q(\zeta_{166})$$ Dimension 0 Newforms 0 Sturm bound 1344 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$4008 = 2^{3} \cdot 3 \cdot 167$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4008.bc (of order $$166$$ and degree $$82$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$2004$$ Character field: $$\Q(\zeta_{166})$$ Newforms: $$0$$ Sturm bound: $$1344$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4008, [\chi])$$.

Total New Old
Modular forms 55760 0 55760
Cusp forms 54448 0 54448
Eisenstein series 1312 0 1312

## Decomposition of $$S_{2}^{\mathrm{old}}(4008, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4008, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(2004, [\chi])$$$$^{\oplus 2}$$