Space of modular forms of level 184, weight 2, and Character 184.b

• Label: 184.2.b
• Level: $184$
• Weight: $2$
• Character orbit: 184.b
• Rep. character: $\chi_{184}(93,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	184.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(184, [\chi])\).

	Total	New	Old
Modular forms	26	22	4
Cusp forms	22	22	0
Eisenstein series	4	0	4

Trace form

\( 22 q + 3 q^{6} + 3 q^{8} - 22 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(184, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
184.2.b.a	$184$	$2$	184.b	8.b	$2$	$2$	$2$	$1.469$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2\beta q^{3}-2q^{4}-\beta q^{5}+4q^{6}+\cdots\)
184.2.b.b	$184$	$2$	184.b	8.b	$2$	$8$	$8$	$1.469$	8.0.5198736512.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{4}q^{3}+\beta _{1}q^{4}-\beta _{6}q^{5}+\cdots\)
184.2.b.c	$184$	$2$	184.b	8.b	$2$	$12$	$12$	$1.469$	12.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)