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

• Label: 184.2.i
• Level: $184$
• Weight: $2$
• Character orbit: 184.i
• Rep. character: $\chi_{184}(9,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $60$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	184.i (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	280	60	220
Cusp forms	200	60	140
Eisenstein series	80	0	80

Trace form

\( 60 q + 2 q^{5} - 2 q^{9} + O(q^{10}) \)

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.i.a	$184$	$2$	184.i	23.c	$11$	$30$	$3$	$1.469$		None		$2$	$0$	\(0\)	\(-2\)	\(2\)	\(13\)		$\mathrm{SU}(2)[C_{11}]$
184.2.i.b	$184$	$2$	184.i	23.c	$11$	$30$	$3$	$1.469$		None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-13\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(184, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(184, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)