# Properties

 Label 1110.2.ba Level $1110$ Weight $2$ Character orbit 1110.ba Rep. character $\chi_{1110}(529,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $72$ Newform subspaces $2$ Sturm bound $456$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.ba (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$185$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$456$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1110, [\chi])$$.

Total New Old
Modular forms 472 72 400
Cusp forms 440 72 368
Eisenstein series 32 0 32

## Trace form

 $$72q - 36q^{4} + 6q^{5} + 36q^{9} + O(q^{10})$$ $$72q - 36q^{4} + 6q^{5} + 36q^{9} + 4q^{10} + 8q^{11} - 36q^{16} + 12q^{19} - 6q^{20} + 2q^{25} + 56q^{26} - 4q^{30} - 60q^{35} - 72q^{36} + 12q^{39} - 2q^{40} + 20q^{41} - 4q^{44} + 20q^{46} + 20q^{49} - 6q^{50} + 96q^{55} + 36q^{59} - 12q^{61} + 72q^{64} + 8q^{65} + 24q^{69} - 20q^{70} - 48q^{71} - 68q^{74} + 16q^{75} - 12q^{76} - 36q^{81} + 52q^{85} + 2q^{90} - 72q^{91} + 24q^{94} - 12q^{95} + 4q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1110, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1110.2.ba.a $$36$$ $$8.863$$ None $$-18$$ $$0$$ $$2$$ $$0$$
1110.2.ba.b $$36$$ $$8.863$$ None $$18$$ $$0$$ $$4$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1110, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1110, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(185, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(370, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(555, [\chi])$$$$^{\oplus 2}$$