# Properties

 Label 46.3.b Level $46$ Weight $3$ Character orbit 46.b Rep. character $\chi_{46}(45,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $18$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$46 = 2 \cdot 23$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 46.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$23$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$18$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(46, [\chi])$$.

Total New Old
Modular forms 14 4 10
Cusp forms 10 4 6
Eisenstein series 4 0 4

## Trace form

 $$4 q - 4 q^{3} + 8 q^{4} + 8 q^{6} - 24 q^{9} + O(q^{10})$$ $$4 q - 4 q^{3} + 8 q^{4} + 8 q^{6} - 24 q^{9} - 8 q^{12} - 4 q^{13} + 16 q^{16} - 16 q^{18} + 52 q^{23} + 16 q^{24} - 132 q^{25} - 64 q^{26} + 44 q^{27} + 84 q^{29} + 116 q^{31} + 56 q^{35} - 48 q^{36} - 60 q^{39} + 20 q^{41} + 56 q^{46} - 28 q^{47} - 16 q^{48} - 148 q^{49} + 176 q^{50} - 8 q^{52} - 104 q^{54} - 56 q^{55} - 80 q^{58} - 184 q^{59} - 24 q^{62} + 32 q^{64} + 4 q^{69} + 288 q^{70} - 100 q^{71} - 32 q^{72} - 148 q^{73} + 308 q^{75} + 344 q^{77} + 56 q^{78} + 68 q^{81} - 48 q^{82} - 120 q^{85} - 164 q^{87} + 104 q^{92} - 140 q^{93} + 136 q^{94} + 352 q^{95} + 32 q^{96} - 400 q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(46, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
46.3.b.a $4$ $1.253$ 4.0.613376.1 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+2q^{4}+\beta _{1}q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(46, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(46, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(23, [\chi])$$$$^{\oplus 2}$$