# Properties

 Label 110.2.k Level $110$ Weight $2$ Character orbit 110.k Rep. character $\chi_{110}(7,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $48$ Newform subspaces $1$ Sturm bound $36$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$110 = 2 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 110.k (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$1$$ Sturm bound: $$36$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(110, [\chi])$$.

Total New Old
Modular forms 176 48 128
Cusp forms 112 48 64
Eisenstein series 64 0 64

## Trace form

 $$48q - 4q^{3} - 8q^{5} - 20q^{7} + O(q^{10})$$ $$48q - 4q^{3} - 8q^{5} - 20q^{7} + 12q^{11} - 16q^{12} - 16q^{15} + 12q^{16} - 20q^{17} - 4q^{20} - 4q^{22} - 8q^{23} - 20q^{25} + 8q^{26} + 8q^{27} - 20q^{28} + 16q^{31} - 104q^{33} - 4q^{36} + 20q^{37} - 36q^{38} - 20q^{41} - 20q^{42} + 16q^{45} + 40q^{46} + 40q^{47} + 4q^{48} + 40q^{50} + 40q^{51} + 40q^{52} + 96q^{55} - 8q^{56} + 48q^{58} + 20q^{60} + 80q^{61} + 40q^{62} + 100q^{63} + 24q^{66} + 20q^{68} - 56q^{70} - 56q^{71} - 20q^{73} - 76q^{75} - 96q^{77} + 16q^{78} - 12q^{80} - 68q^{81} - 80q^{85} - 56q^{86} - 4q^{88} - 80q^{90} - 68q^{91} - 12q^{92} + 76q^{93} + 20q^{95} + 72q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(110, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
110.2.k.a $$48$$ $$0.878$$ None $$0$$ $$-4$$ $$-8$$ $$-20$$

## Decomposition of $$S_{2}^{\mathrm{old}}(110, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(110, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 2}$$