# Properties

 Label 2850.2.n Level $2850$ Weight $2$ Character orbit 2850.n Rep. character $\chi_{2850}(571,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $368$ 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.n (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{5})$$ Sturm bound: $$1200$$

## Dimensions

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

Total New Old
Modular forms 2432 368 2064
Cusp forms 2368 368 2000
Eisenstein series 64 0 64

## Trace form

 $$368q - 4q^{2} - 92q^{4} - 8q^{5} - 4q^{6} - 16q^{7} - 4q^{8} - 92q^{9} + O(q^{10})$$ $$368q - 4q^{2} - 92q^{4} - 8q^{5} - 4q^{6} - 16q^{7} - 4q^{8} - 92q^{9} - 8q^{10} + 12q^{11} - 8q^{13} - 4q^{15} - 92q^{16} + 4q^{17} + 16q^{18} - 4q^{19} + 12q^{20} - 8q^{22} + 12q^{23} + 16q^{24} - 12q^{25} - 24q^{26} + 4q^{28} - 24q^{29} + 12q^{31} + 16q^{32} - 8q^{33} + 36q^{34} - 12q^{35} - 92q^{36} - 36q^{37} - 8q^{40} + 48q^{41} + 12q^{42} - 8q^{43} - 8q^{44} - 8q^{45} - 56q^{47} + 416q^{49} - 20q^{50} - 8q^{52} + 60q^{53} - 4q^{54} - 40q^{55} - 48q^{58} + 16q^{60} - 56q^{61} + 72q^{62} + 4q^{63} - 92q^{64} - 52q^{65} - 16q^{66} - 32q^{67} - 16q^{68} + 52q^{70} - 4q^{72} + 24q^{73} - 56q^{74} - 32q^{75} + 16q^{76} - 112q^{77} + 40q^{79} - 8q^{80} - 92q^{81} + 120q^{82} + 12q^{83} + 48q^{85} - 48q^{86} - 56q^{87} + 12q^{88} + 36q^{89} - 8q^{90} - 8q^{91} - 8q^{92} - 32q^{93} - 4q^{95} - 4q^{96} - 92q^{97} - 36q^{98} - 8q^{99} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(2850, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(475, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(950, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1425, [\chi])$$$$^{\oplus 2}$$