# Properties

 Label 2850.2.bt Level $2850$ Weight $2$ Character orbit 2850.bt Rep. character $\chi_{2850}(619,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $800$ 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.bt (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$475$$ 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 800 4064
Cusp forms 4736 800 3936
Eisenstein series 128 0 128

## Trace form

 $$800q - 100q^{4} - 4q^{5} - 100q^{9} + O(q^{10})$$ $$800q - 100q^{4} - 4q^{5} - 100q^{9} + 24q^{11} - 4q^{15} + 100q^{16} + 20q^{17} + 12q^{19} - 8q^{20} + 8q^{21} - 20q^{22} - 60q^{23} + 8q^{25} - 24q^{29} + 32q^{30} - 20q^{33} - 16q^{34} + 4q^{35} + 100q^{36} - 8q^{44} - 8q^{45} + 16q^{46} - 40q^{47} - 784q^{49} - 32q^{51} - 80q^{53} + 140q^{55} - 72q^{59} + 4q^{60} + 32q^{61} - 20q^{63} + 200q^{64} + 8q^{65} + 80q^{67} + 16q^{69} - 12q^{70} - 8q^{71} - 80q^{73} - 16q^{75} + 8q^{76} - 160q^{77} + 16q^{79} - 4q^{80} + 100q^{81} - 160q^{83} + 16q^{84} - 36q^{85} - 80q^{87} + 24q^{89} + 16q^{91} + 32q^{94} + 52q^{95} + 60q^{97} + 80q^{98} - 8q^{99} + O(q^{100})$$

## 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

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