# Properties

 Label 23.3.b Level 23 Weight 3 Character orbit b Rep. character $$\chi_{23}(22,\cdot)$$ Character field $$\Q$$ Dimension 3 Newforms 1 Sturm bound 6 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$23$$ Weight: $$k$$ = $$3$$ Character orbit: $$[\chi]$$ = 23.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$23$$ Character field: $$\Q$$ Newforms: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(23, [\chi])$$.

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

## Trace form

 $$3q + 12q^{4} - 33q^{6} - 21q^{8} + 27q^{9} + O(q^{10})$$ $$3q + 12q^{4} - 33q^{6} - 21q^{8} + 27q^{9} + 3q^{12} + 48q^{16} + 39q^{18} - 69q^{23} - 132q^{24} + 75q^{25} + 87q^{26} - 114q^{27} - 84q^{32} + 255q^{36} - 42q^{39} + 231q^{48} + 147q^{49} - 309q^{52} - 297q^{54} - 273q^{58} + 78q^{59} + 303q^{62} - 45q^{64} - 33q^{72} + 399q^{78} + 243q^{81} - 129q^{82} + 246q^{87} - 276q^{92} - 546q^{93} - 57q^{94} - 21q^{96} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(23, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
23.3.b.a $$3$$ $$0.627$$ 3.3.621.1 $$\Q(\sqrt{-23})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots$$