Properties

 Label 110.2.b Level $110$ Weight $2$ Character orbit 110.b Rep. character $\chi_{110}(89,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $3$ Sturm bound $36$ Trace bound $5$

Related objects

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 22 6 16
Cusp forms 14 6 8
Eisenstein series 8 0 8

Trace form

 $$6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} - 10 q^{9} + O(q^{10})$$ $$6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} - 10 q^{9} + 4 q^{10} + 2 q^{11} - 4 q^{14} - 4 q^{15} + 6 q^{16} + 16 q^{19} - 2 q^{20} + 4 q^{24} + 6 q^{25} + 4 q^{26} + 4 q^{29} - 4 q^{30} - 12 q^{31} - 8 q^{34} - 8 q^{35} + 10 q^{36} + 16 q^{39} - 4 q^{40} - 36 q^{41} - 2 q^{44} - 34 q^{45} - 12 q^{46} + 22 q^{49} + 24 q^{50} + 48 q^{51} + 16 q^{54} - 6 q^{55} + 4 q^{56} + 4 q^{60} - 36 q^{61} - 6 q^{64} + 16 q^{65} + 8 q^{66} - 32 q^{69} + 16 q^{70} - 20 q^{71} + 16 q^{75} - 16 q^{76} - 16 q^{79} + 2 q^{80} - 2 q^{81} + 8 q^{85} + 8 q^{86} + 8 q^{89} - 20 q^{90} + 24 q^{91} - 20 q^{94} - 4 q^{96} + 14 q^{99} + O(q^{100})$$

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.b.a $2$ $0.878$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}+(-2+i)q^{5}+\cdots$$
110.2.b.b $2$ $0.878$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{2}-2iq^{3}-q^{4}+(1-2i)q^{5}+\cdots$$
110.2.b.c $2$ $0.878$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{2}+3iq^{3}-q^{4}+(2-i)q^{5}-3q^{6}+\cdots$$

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

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