# Properties

 Label 110.2.j Level $110$ Weight $2$ Character orbit 110.j Rep. character $\chi_{110}(9,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $24$ Newform subspaces $2$ Sturm bound $36$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$110 = 2 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 110.j (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$2$$ Sturm bound: $$36$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 88 24 64
Cusp forms 56 24 32
Eisenstein series 32 0 32

## Trace form

 $$24q + 6q^{4} - 2q^{5} + 4q^{6} - 10q^{9} + O(q^{10})$$ $$24q + 6q^{4} - 2q^{5} + 4q^{6} - 10q^{9} - 4q^{10} - 2q^{11} - 6q^{14} + 14q^{15} - 6q^{16} - 16q^{19} + 2q^{20} - 40q^{21} - 4q^{24} - 6q^{25} - 4q^{26} - 4q^{29} - 26q^{30} - 8q^{31} + 8q^{34} - 52q^{35} - 10q^{36} - 36q^{39} - 6q^{40} + 46q^{41} + 22q^{44} + 44q^{45} + 32q^{46} + 68q^{49} - 4q^{50} + 12q^{51} + 64q^{54} + 36q^{55} - 4q^{56} + 16q^{60} + 56q^{61} + 6q^{64} + 44q^{65} - 68q^{66} + 32q^{69} + 24q^{70} - 60q^{71} + 64q^{75} - 4q^{76} - 4q^{79} + 8q^{80} - 138q^{81} - 20q^{84} - 38q^{85} - 8q^{86} - 108q^{89} + 10q^{90} - 14q^{91} - 30q^{94} - 50q^{95} + 4q^{96} + 6q^{99} + O(q^{100})$$

## 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.j.a $$8$$ $$0.878$$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\zeta_{20}q^{2}+(-2\zeta_{20}-2\zeta_{20}^{5})q^{3}+\cdots$$
110.2.j.b $$16$$ $$0.878$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-6$$ $$0$$ $$q-\beta _{6}q^{2}+(-\beta _{6}-\beta _{10}-\beta _{12})q^{3}+\cdots$$

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

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