# Properties

 Label 185.2.b Level $185$ Weight $2$ Character orbit 185.b Rep. character $\chi_{185}(149,\cdot)$ Character field $\Q$ Dimension $18$ Newform subspaces $1$ Sturm bound $38$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$185 = 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 185.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$38$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(185, [\chi])$$.

Total New Old
Modular forms 22 18 4
Cusp forms 18 18 0
Eisenstein series 4 0 4

## Trace form

 $$18 q - 22 q^{4} + 2 q^{5} + 4 q^{6} - 26 q^{9} + O(q^{10})$$ $$18 q - 22 q^{4} + 2 q^{5} + 4 q^{6} - 26 q^{9} + 6 q^{10} + 8 q^{14} - 2 q^{15} + 22 q^{16} + 8 q^{19} - 4 q^{20} + 8 q^{21} - 12 q^{24} - 18 q^{25} - 12 q^{26} + 4 q^{29} - 12 q^{31} - 12 q^{34} - 2 q^{35} + 22 q^{36} + 32 q^{39} - 6 q^{40} + 4 q^{41} - 8 q^{44} - 16 q^{45} + 32 q^{46} + 14 q^{49} + 8 q^{50} + 16 q^{51} + 36 q^{54} - 34 q^{55} - 48 q^{56} - 20 q^{59} + 28 q^{60} + 16 q^{61} - 30 q^{64} + 20 q^{65} - 68 q^{66} + 20 q^{69} + 40 q^{70} + 16 q^{71} + 10 q^{74} - 56 q^{75} - 96 q^{76} + 52 q^{79} + 36 q^{80} + 26 q^{81} + 48 q^{84} - 8 q^{85} - 32 q^{86} + 16 q^{89} - 86 q^{90} - 36 q^{91} + 52 q^{94} - 44 q^{95} + 104 q^{96} - 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(185, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
185.2.b.a $18$ $1.477$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(\beta _{1}+\beta _{13})q^{2}+(\beta _{12}-\beta _{13})q^{3}+(-2+\cdots)q^{4}+\cdots$$