# Properties

 Label 92.2.b Level $92$ Weight $2$ Character orbit 92.b Rep. character $\chi_{92}(91,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $2$ Sturm bound $24$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$92 = 2^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 92.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$92$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(92, [\chi])$$.

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

## Trace form

 $$10 q - 4 q^{2} + q^{6} - q^{8} - 10 q^{9} + O(q^{10})$$ $$10 q - 4 q^{2} + q^{6} - q^{8} - 10 q^{9} + 7 q^{12} - 4 q^{13} - 16 q^{16} + 13 q^{18} + 8 q^{24} - 6 q^{25} - 23 q^{26} + 20 q^{29} + 16 q^{32} - 33 q^{36} - 12 q^{41} + 12 q^{46} + 39 q^{48} - 14 q^{49} + 36 q^{50} + 3 q^{52} + 29 q^{54} - 35 q^{58} + 25 q^{62} - 21 q^{64} - 12 q^{69} - 56 q^{70} + 43 q^{72} - 4 q^{73} - 56 q^{77} - 55 q^{78} + 58 q^{81} + 45 q^{82} + 56 q^{85} - 24 q^{92} + 8 q^{93} - 27 q^{94} - 73 q^{96} - 28 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(92, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
92.2.b.a $4$ $0.735$ $$\Q(i, \sqrt{14})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-1-\beta _{1})q^{2}+\beta _{1}q^{3}+2\beta _{1}q^{4}+\cdots$$
92.2.b.b $6$ $0.735$ 6.0.8869743.1 $$\Q(\sqrt{-23})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$$