# Properties

 Label 22.3.b Level 22 Weight 3 Character orbit b Rep. character $$\chi_{22}(21,\cdot)$$ Character field $$\Q$$ Dimension 2 Newforms 1 Sturm bound 9 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$22 = 2 \cdot 11$$ Weight: $$k$$ = $$3$$ Character orbit: $$[\chi]$$ = 22.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$11$$ Character field: $$\Q$$ Newforms: $$1$$ Sturm bound: $$9$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(22, [\chi])$$.

Total New Old
Modular forms 8 2 6
Cusp forms 4 2 2
Eisenstein series 4 0 4

## Trace form

 $$2q + 2q^{3} - 4q^{4} - 2q^{5} - 16q^{9} + O(q^{10})$$ $$2q + 2q^{3} - 4q^{4} - 2q^{5} - 16q^{9} + 14q^{11} - 4q^{12} + 24q^{14} - 2q^{15} + 8q^{16} + 4q^{20} - 24q^{22} + 34q^{23} - 48q^{25} - 24q^{26} - 34q^{27} + 34q^{31} + 14q^{33} - 72q^{34} + 32q^{36} + 94q^{37} + 72q^{38} + 24q^{42} - 28q^{44} + 16q^{45} - 116q^{47} + 8q^{48} - 46q^{49} + 4q^{53} - 14q^{55} - 48q^{56} + 96q^{58} - 110q^{59} + 4q^{60} - 16q^{64} - 24q^{66} + 178q^{67} + 34q^{69} - 24q^{70} - 14q^{71} - 48q^{75} + 144q^{77} - 24q^{78} - 8q^{80} + 110q^{81} - 24q^{82} - 48q^{86} + 48q^{88} - 194q^{89} + 144q^{91} - 68q^{92} + 34q^{93} - 242q^{97} - 112q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(22, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
22.3.b.a $$2$$ $$0.599$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$-2$$ $$0$$ $$q+\beta q^{2}+q^{3}-2q^{4}-q^{5}+\beta q^{6}-6\beta q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(22, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(22, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(11, [\chi])$$$$^{\oplus 2}$$