# Properties

 Label 2240.2.dk Level $2240$ Weight $2$ Character orbit 2240.dk Rep. character $\chi_{2240}(767,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $368$ Sturm bound $768$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2240 = 2^{6} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2240.dk (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$140$$ 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 1632 400 1232
Cusp forms 1440 368 1072
Eisenstein series 192 32 160

## Trace form

 $$368q + 4q^{5} + O(q^{10})$$ $$368q + 4q^{5} + 16q^{13} - 4q^{17} + 16q^{21} - 4q^{25} - 28q^{33} + 4q^{37} - 32q^{41} + 44q^{45} + 4q^{53} + 8q^{57} + 8q^{61} - 4q^{65} - 4q^{73} + 84q^{77} + 144q^{81} + 112q^{85} + 28q^{93} + 48q^{97} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(2240, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(560, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1120, [\chi])$$$$^{\oplus 2}$$