# Properties

 Label 1140.2.z Level $1140$ Weight $2$ Character orbit 1140.z Rep. character $\chi_{1140}(449,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $80$ Newform subspaces $1$ Sturm bound $480$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1140.z (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$285$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$480$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 504 80 424
Cusp forms 456 80 376
Eisenstein series 48 0 48

## Trace form

 $$80q + O(q^{10})$$ $$80q + 3q^{15} - 4q^{19} + 2q^{25} + 6q^{45} - 56q^{49} + 54q^{51} - 12q^{55} + 12q^{61} + 24q^{79} - 4q^{81} + 10q^{85} + 60q^{91} + 12q^{99} + O(q^{100})$$

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

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1140.2.z.a $$80$$ $$9.103$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(1140, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(570, [\chi])$$$$^{\oplus 2}$$