Space of modular forms of level 184, weight 3, and Character 184.g

• Label: 184.3.g
• Level: $184$
• Weight: $3$
• Character orbit: 184.g
• Rep. character: $\chi_{184}(139,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	184.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(184, [\chi])\).

	Total	New	Old
Modular forms	50	44	6
Cusp forms	46	44	2
Eisenstein series	4	0	4

Trace form

44 * q - 3 * q^6 + 15 * q^8 + 132 * q^9 + 26 * q^10 - 19 * q^12 - 8 * q^14 - 16 * q^16 - 8 * q^17 - 57 * q^18 + 40 * q^20 + 44 * q^22 - 88 * q^24 - 244 * q^25 + 19 * q^26 - 48 * q^27 + 6 * q^28 + 86 * q^30 + 160 * q^32 + 16 * q^33 + 18 * q^34 + 96 * q^35 + 179 * q^36 - 156 * q^38 + 130 * q^40 + 88 * q^41 + 100 * q^42 - 128 * q^43 - 158 * q^44 + 5 * q^48 - 340 * q^49 + 4 * q^50 + 160 * q^51 - 127 * q^52 + 53 * q^54 - 6 * q^56 - 176 * q^57 + 147 * q^58 + 16 * q^59 - 283 * q^62 - 405 * q^64 + 96 * q^65 - 602 * q^66 - 288 * q^67 + 72 * q^68 + 312 * q^70 - 57 * q^72 + 280 * q^73 - 198 * q^74 + 160 * q^75 + 172 * q^76 - 185 * q^78 - 90 * q^80 + 284 * q^81 - 75 * q^82 - 480 * q^83 - 254 * q^84 - 98 * q^86 + 204 * q^88 - 200 * q^89 + 488 * q^90 + 192 * q^91 + 19 * q^94 - 107 * q^96 + 184 * q^97 + 200 * q^98 + 256 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(184, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
184.3.g.a	$184$	$3$	184.g	8.d	$2$	$44$	$44$	$5.014$		None		✓	✓	✓	184.3.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(184, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(184, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)