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 - 2 * q^11 - 4 * q^15 + 4 * q^17 - 2 * q^19 + 4 * q^21 + 2 * q^25 - 12 * q^27 - 12 * q^29 + 12 * q^31 + 12 * q^33 - 22 * q^35 - 26 * q^37 - 16 * q^39 - 26 * q^41 - 34 * q^43 - 84 * q^45 - 48 * q^47 - 64 * q^49 - 48 * q^51 - 16 * q^53 - 68 * q^55 - 44 * q^57 - 22 * q^59 + 26 * q^61 + 20 * q^63 - 16 * q^65 - 6 * q^67 - 4 * q^69 - 4 * q^71 + 20 * q^73 + 90 * q^75 - 24 * q^77 + 62 * q^79 + 126 * q^81 + 52 * q^83 + 46 * q^85 + 170 * q^87 + 54 * q^89 + 168 * q^91 - 28 * q^93 + 140 * q^95 + 78 * q^97 + 184 * q^99

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

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

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