# Properties

 Label 2850.2.cp Level $2850$ Weight $2$ Character orbit 2850.cp Rep. character $\chi_{2850}(139,\cdot)$ Character field $\Q(\zeta_{90})$ Dimension $2400$ 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.cp (of order $$90$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$475$$ Character field: $$\Q(\zeta_{90})$$ Sturm bound: $$1200$$

## Dimensions

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

Total New Old
Modular forms 14592 2400 12192
Cusp forms 14208 2400 11808
Eisenstein series 384 0 384

## Trace form

 $$2400q + O(q^{10})$$ $$2400q - 36q^{11} - 24q^{15} - 24q^{20} + 60q^{22} + 120q^{23} + 108q^{25} + 72q^{29} + 60q^{33} - 24q^{35} + 12q^{45} + 84q^{46} + 120q^{47} + 1176q^{49} - 108q^{55} + 72q^{59} - 12q^{60} + 144q^{61} - 300q^{64} - 48q^{69} + 72q^{70} + 24q^{71} + 96q^{79} + 60q^{83} - 24q^{84} + 240q^{85} - 60q^{87} + 144q^{89} + 192q^{94} + 60q^{95} + 360q^{97} + 480q^{98} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(2850, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(475, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(950, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1425, [\chi])$$$$^{\oplus 2}$$