# Properties

 Label 110.2.g Level $110$ Weight $2$ Character orbit 110.g Rep. character $\chi_{110}(31,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $16$ Newform subspaces $3$ Sturm bound $36$ Trace bound $2$

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## Defining parameters

 Level: $$N$$ $$=$$ $$110 = 2 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 110.g (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$3$$ Sturm bound: $$36$$ Trace bound: $$2$$ 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 16 72
Cusp forms 56 16 40
Eisenstein series 32 0 32

## Trace form

 $$16q + 2q^{2} + 4q^{3} - 4q^{4} - 6q^{6} + 2q^{8} - 12q^{9} + O(q^{10})$$ $$16q + 2q^{2} + 4q^{3} - 4q^{4} - 6q^{6} + 2q^{8} - 12q^{9} - 8q^{10} - 8q^{11} + 4q^{12} - 8q^{13} + 2q^{14} - 12q^{15} - 4q^{16} + 8q^{17} + 16q^{18} - 14q^{19} + 48q^{21} + 10q^{22} + 16q^{23} - 6q^{24} - 4q^{25} - 16q^{26} - 26q^{27} - 40q^{29} + 4q^{30} - 4q^{31} - 8q^{32} + 34q^{33} - 12q^{34} + 8q^{35} - 2q^{36} - 16q^{37} + 16q^{38} - 32q^{39} + 2q^{40} - 30q^{41} - 16q^{42} + 12q^{43} + 2q^{44} - 8q^{46} + 24q^{47} + 4q^{48} + 30q^{49} + 2q^{50} + 10q^{51} + 12q^{52} + 16q^{54} - 8q^{55} + 12q^{56} + 70q^{57} + 28q^{58} + 54q^{59} + 8q^{60} - 24q^{61} + 4q^{62} - 44q^{63} - 4q^{64} - 20q^{65} + 28q^{66} - 12q^{67} + 8q^{68} - 20q^{69} - 12q^{71} - 14q^{72} - 24q^{73} - 4q^{74} - 6q^{75} + 16q^{76} - 32q^{78} + 2q^{81} - 18q^{82} - 34q^{83} - 12q^{84} + 28q^{85} + 22q^{86} - 48q^{87} - 10q^{88} + 48q^{89} + 26q^{90} + 50q^{91} - 24q^{92} - 16q^{93} - 26q^{94} + 4q^{96} - 10q^{97} - 8q^{98} + 76q^{99} + O(q^{100})$$

## 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.g.a $$4$$ $$0.878$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$4$$ $$1$$ $$1$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
110.2.g.b $$4$$ $$0.878$$ $$\Q(\zeta_{10})$$ None $$1$$ $$4$$ $$1$$ $$0$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots$$
110.2.g.c $$8$$ $$0.878$$ 8.0.682515625.5 None $$2$$ $$-4$$ $$-2$$ $$-1$$ $$q+(1-\beta _{2}+\beta _{3}-\beta _{7})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(110, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(22, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 2}$$