# Properties

 Label 1140.2.ca Level $1140$ Weight $2$ Character orbit 1140.ca Rep. character $\chi_{1140}(79,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $720$ Sturm bound $480$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1140.ca (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$380$$ Character field: $$\Q(\zeta_{18})$$ Sturm bound: $$480$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1140, [\chi])$$.

Total New Old
Modular forms 1488 720 768
Cusp forms 1392 720 672
Eisenstein series 96 0 96

## Trace form

 $$720q + 6q^{4} + 6q^{6} + O(q^{10})$$ $$720q + 6q^{4} + 6q^{6} + 18q^{10} - 36q^{14} - 6q^{16} + 60q^{20} - 6q^{34} - 6q^{36} + 114q^{40} - 24q^{41} - 360q^{49} + 54q^{50} - 6q^{54} - 6q^{64} + 144q^{69} + 36q^{70} - 96q^{74} + 36q^{76} - 18q^{80} - 108q^{84} + 24q^{85} - 120q^{86} + 48q^{89} + 18q^{90} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1140, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1140, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1140, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(380, [\chi])$$$$^{\oplus 2}$$