# Properties

 Label 1140.2.u Level $1140$ Weight $2$ Character orbit 1140.u Rep. character $\chi_{1140}(77,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $72$ Newform subspaces $2$ Sturm bound $480$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1140.u (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$480$$ Trace bound: $$7$$

## Dimensions

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

Total New Old
Modular forms 504 72 432
Cusp forms 456 72 384
Eisenstein series 48 0 48

## Trace form

 $$72q - 4q^{3} + 8q^{7} + O(q^{10})$$ $$72q - 4q^{3} + 8q^{7} + 16q^{13} + 8q^{15} + 8q^{21} - 24q^{25} - 16q^{27} - 16q^{31} - 16q^{33} + 40q^{37} + 16q^{43} - 24q^{51} + 32q^{55} + 32q^{61} - 8q^{63} + 8q^{67} - 24q^{73} - 32q^{75} + 40q^{81} - 72q^{85} - 32q^{91} + 40q^{93} - 56q^{97} + O(q^{100})$$

## 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.u.a $$36$$ $$9.103$$ None $$0$$ $$-2$$ $$0$$ $$-4$$
1140.2.u.b $$36$$ $$9.103$$ None $$0$$ $$-2$$ $$0$$ $$12$$

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

$$S_{2}^{\mathrm{old}}(1140, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(570, [\chi])$$$$^{\oplus 2}$$