# Properties

 Label 1110.2.ch Level $1110$ Weight $2$ Character orbit 1110.ch Rep. character $\chi_{1110}(13,\cdot)$ Character field $\Q(\zeta_{36})$ Dimension $456$ Sturm bound $456$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.ch (of order $$36$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$185$$ Character field: $$\Q(\zeta_{36})$$ Sturm bound: $$456$$

## Dimensions

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

Total New Old
Modular forms 2832 456 2376
Cusp forms 2640 456 2184
Eisenstein series 192 0 192

## Trace form

 $$456q + O(q^{10})$$ $$456q + 48q^{14} + 12q^{17} - 12q^{25} + 48q^{30} - 24q^{31} + 192q^{35} + 24q^{37} - 48q^{39} + 24q^{40} + 60q^{41} + 24q^{44} - 96q^{49} - 96q^{50} - 72q^{53} + 72q^{57} + 60q^{58} + 168q^{61} + 48q^{62} + 228q^{64} - 72q^{65} + 48q^{67} + 24q^{70} + 96q^{71} - 12q^{73} - 60q^{74} - 24q^{76} + 72q^{77} + 48q^{79} + 192q^{83} - 48q^{86} - 24q^{88} - 24q^{89} + 24q^{93} + 24q^{95} - 96q^{97} + 48q^{98} + O(q^{100})$$

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

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

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

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