# Properties

 Label 2850.2.cr Level $2850$ Weight $2$ Character orbit 2850.cr Rep. character $\chi_{2850}(17,\cdot)$ Character field $\Q(\zeta_{180})$ Dimension $9600$ 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.cr (of order $$180$$ and degree $$48$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1425$$ Character field: $$\Q(\zeta_{180})$$ Sturm bound: $$1200$$

## Dimensions

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

Total New Old
Modular forms 29184 9600 19584
Cusp forms 28416 9600 18816
Eisenstein series 768 0 768

## Trace form

 $$9600q + O(q^{10})$$ $$9600q + 36q^{15} + 48q^{18} + 96q^{22} + 24q^{25} - 72q^{33} - 24q^{43} + 36q^{45} + 120q^{55} + 132q^{57} + 48q^{60} + 36q^{63} - 48q^{67} + 48q^{70} + 48q^{78} + 180q^{84} - 192q^{85} + 96q^{87} + 168q^{90} + 228q^{93} - 48q^{97} + O(q^{100})$$

## 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

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