# Properties

 Label 2240.2.df Level $2240$ Weight $2$ Character orbit 2240.df Rep. character $\chi_{2240}(81,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $256$ Sturm bound $768$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2240 = 2^{6} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2240.df (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$112$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$768$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2240, [\chi])$$.

Total New Old
Modular forms 1600 256 1344
Cusp forms 1472 256 1216
Eisenstein series 128 0 128

## Trace form

 $$256q + O(q^{10})$$ $$256q - 8q^{11} - 32q^{29} + 16q^{37} - 16q^{43} - 80q^{47} + 40q^{51} - 16q^{53} - 16q^{59} + 40q^{67} + 128q^{81} + 80q^{83} + 32q^{91} + 80q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2240, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{2}^{\mathrm{old}}(2240, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2240, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(448, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(560, [\chi])$$$$^{\oplus 3}$$