# Properties

 Label 2850.2.bw Level $2850$ Weight $2$ Character orbit 2850.bw Rep. character $\chi_{2850}(179,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $1600$ Sturm bound $1200$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2850.bw (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1425$$ Character field: $$\Q(\zeta_{30})$$ Sturm bound: $$1200$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2850, [\chi])$$.

Total New Old
Modular forms 4864 1600 3264
Cusp forms 4736 1600 3136
Eisenstein series 128 0 128

## Trace form

 $$1600q - 200q^{4} + O(q^{10})$$ $$1600q - 200q^{4} + 30q^{15} + 200q^{16} - 12q^{19} + 60q^{22} + 12q^{25} + 4q^{30} + 24q^{39} + 28q^{45} - 1536q^{49} + 60q^{51} + 12q^{54} - 12q^{55} - 30q^{60} - 24q^{61} + 40q^{63} + 400q^{64} + 16q^{66} - 36q^{70} + 80q^{73} - 8q^{76} - 8q^{81} - 32q^{85} + 54q^{90} + 32q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2850, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(2850, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2850, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(1425, [\chi])$$$$^{\oplus 2}$$