# Properties

 Label 2240.2.fg Level $2240$ Weight $2$ Character orbit 2240.fg Rep. character $\chi_{2240}(109,\cdot)$ Character field $\Q(\zeta_{48})$ Dimension $6080$ Sturm bound $768$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2240 = 2^{6} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2240.fg (of order $$48$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$2240$$ Character field: $$\Q(\zeta_{48})$$ Sturm bound: $$768$$

## Dimensions

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

Total New Old
Modular forms 6208 6208 0
Cusp forms 6080 6080 0
Eisenstein series 128 128 0

## Trace form

 $$6080q - 16q^{4} - 8q^{5} - 64q^{6} - 16q^{9} + O(q^{10})$$ $$6080q - 16q^{4} - 8q^{5} - 64q^{6} - 16q^{9} - 8q^{10} - 16q^{11} - 32q^{14} - 32q^{15} - 16q^{16} - 16q^{19} - 32q^{20} - 32q^{21} - 16q^{24} - 8q^{25} - 16q^{26} - 64q^{29} - 88q^{30} - 64q^{34} - 16q^{35} - 384q^{36} - 16q^{39} - 8q^{40} - 64q^{41} - 16q^{44} - 8q^{45} - 16q^{46} - 32q^{49} - 80q^{50} - 16q^{51} - 16q^{54} - 32q^{55} - 32q^{56} - 80q^{59} - 104q^{60} - 16q^{61} - 256q^{64} - 16q^{65} - 48q^{66} - 64q^{69} - 16q^{70} - 192q^{71} - 112q^{74} - 8q^{75} - 64q^{76} - 16q^{79} + 16q^{80} - 16q^{81} + 80q^{84} - 32q^{85} - 16q^{86} - 16q^{89} - 32q^{90} - 32q^{91} - 16q^{94} - 16q^{96} + 32q^{99} + O(q^{100})$$

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

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