# Properties

 Label 1840.2.bg Level $1840$ Weight $2$ Character orbit 1840.bg Rep. character $\chi_{1840}(829,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $528$ Sturm bound $576$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1840 = 2^{4} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1840.bg (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$80$$ Character field: $$\Q(i)$$ Sturm bound: $$576$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1840, [\chi])$$.

Total New Old
Modular forms 584 528 56
Cusp forms 568 528 40
Eisenstein series 16 0 16

## Trace form

 $$528q + O(q^{10})$$ $$528q + 12q^{10} - 16q^{14} + 28q^{20} + 32q^{24} - 32q^{26} + 52q^{30} - 48q^{31} + 24q^{35} - 80q^{36} - 40q^{44} + 528q^{49} - 12q^{50} + 56q^{54} - 32q^{59} - 116q^{60} - 24q^{64} + 16q^{65} + 200q^{66} - 108q^{70} + 88q^{74} - 88q^{75} + 120q^{76} - 28q^{80} - 528q^{81} + 96q^{84} + 64q^{86} + 124q^{90} - 32q^{91} + 56q^{94} - 48q^{95} - 40q^{96} - 64q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1840, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1840, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1840, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 2}$$