# Properties

 Label 2850.2.k Level $2850$ Weight $2$ Character orbit 2850.k Rep. character $\chi_{2850}(2243,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $216$ 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.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Sturm bound: $$1200$$

## Dimensions

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

Total New Old
Modular forms 1248 216 1032
Cusp forms 1152 216 936
Eisenstein series 96 0 96

## Trace form

 $$216q - 8q^{3} - 16q^{6} - 8q^{7} + O(q^{10})$$ $$216q - 8q^{3} - 16q^{6} - 8q^{7} + 8q^{12} - 16q^{13} - 216q^{16} + 32q^{21} + 8q^{22} + 16q^{27} - 8q^{28} + 32q^{31} - 32q^{33} - 16q^{36} + 32q^{37} - 24q^{42} + 32q^{43} + 64q^{46} + 8q^{48} + 16q^{52} - 40q^{58} - 160q^{61} - 16q^{63} - 80q^{67} + 24q^{73} + 40q^{78} - 128q^{81} - 32q^{82} + 8q^{88} - 128q^{91} + 56q^{93} + 16q^{96} + 56q^{97} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(2850, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(570, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1425, [\chi])$$$$^{\oplus 2}$$