# Properties

 Label 1110.2.o Level $1110$ Weight $2$ Character orbit 1110.o Rep. character $\chi_{1110}(253,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $76$ Newform subspaces $2$ Sturm bound $456$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.o (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$185$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$456$$ Trace bound: $$1$$

## Dimensions

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

Total New Old
Modular forms 472 76 396
Cusp forms 440 76 364
Eisenstein series 32 0 32

## Trace form

 $$76q + 4q^{2} + 76q^{4} + 4q^{5} + 4q^{8} + O(q^{10})$$ $$76q + 4q^{2} + 76q^{4} + 4q^{5} + 4q^{8} - 4q^{10} - 8q^{14} + 76q^{16} - 8q^{19} + 4q^{20} - 4q^{25} + 16q^{26} - 36q^{29} + 24q^{31} + 4q^{32} + 40q^{35} + 36q^{37} - 8q^{39} - 4q^{40} - 32q^{43} - 12q^{50} + 16q^{51} + 12q^{53} - 16q^{55} - 8q^{56} - 16q^{57} + 36q^{58} + 8q^{59} - 12q^{61} + 32q^{62} + 76q^{64} - 48q^{65} - 8q^{66} - 32q^{67} + 16q^{69} - 16q^{70} + 32q^{71} - 4q^{73} - 20q^{74} + 32q^{75} - 8q^{76} + 16q^{77} + 24q^{79} + 4q^{80} - 76q^{81} + 32q^{86} + 12q^{89} + 32q^{91} - 16q^{93} - 32q^{94} + 48q^{95} + O(q^{100})$$

## 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.o.a $$36$$ $$8.863$$ None $$-36$$ $$0$$ $$4$$ $$4$$
1110.2.o.b $$40$$ $$8.863$$ None $$40$$ $$0$$ $$0$$ $$-4$$

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

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