Space of modular forms of level 185, weight 2, and Character 185.b

• 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: $0$

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

\( 18 q - 22 q^{4} + 2 q^{5} + 4 q^{6} - 26 q^{9} + O(q^{10}) \)

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
185.2.b.a	$185$	$2$	185.b	5.b	$2$	$18$	$18$	$1.477$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{13})q^{2}+(\beta _{12}-\beta _{13})q^{3}+(-2+\cdots)q^{4}+\cdots\)