# Properties

 Label 1110.2.bb Level $1110$ Weight $2$ Character orbit 1110.bb Rep. character $\chi_{1110}(1009,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $80$ Newform subspaces $5$ Sturm bound $456$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.bb (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$185$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$456$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

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

Total New Old
Modular forms 472 80 392
Cusp forms 440 80 360
Eisenstein series 32 0 32

## Trace form

 $$80q + 40q^{4} + 40q^{9} + O(q^{10})$$ $$80q + 40q^{4} + 40q^{9} + 8q^{11} + 16q^{14} - 40q^{16} - 12q^{19} - 16q^{21} - 4q^{25} - 24q^{26} - 32q^{29} - 4q^{30} - 32q^{31} + 28q^{34} - 4q^{35} + 80q^{36} + 12q^{39} + 40q^{41} + 4q^{44} - 4q^{46} + 72q^{49} + 32q^{50} + 16q^{51} + 8q^{55} + 8q^{56} - 52q^{59} + 16q^{61} - 80q^{64} + 60q^{65} + 8q^{66} + 8q^{69} - 20q^{70} - 32q^{71} - 28q^{74} + 16q^{75} + 12q^{76} - 8q^{79} - 40q^{81} - 32q^{84} + 16q^{85} - 16q^{86} + 20q^{89} + 16q^{91} - 8q^{94} - 28q^{95} + 4q^{99} + O(q^{100})$$

## 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.bb.a $$4$$ $$8.863$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots$$
1110.2.bb.b $$4$$ $$8.863$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
1110.2.bb.c $$4$$ $$8.863$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots$$
1110.2.bb.d $$28$$ $$8.863$$ None $$0$$ $$0$$ $$2$$ $$0$$
1110.2.bb.e $$40$$ $$8.863$$ None $$0$$ $$0$$ $$2$$ $$0$$

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

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