Space of modular forms of level 231, weight 4, and Character 231.l

• Label: 231.4.l
• Level: $231$
• Weight: $4$
• Character orbit: 231.l
• Rep. character: $\chi_{231}(32,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $184$
• Newform subspaces: $1$
• Sturm bound: $128$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	231.l (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 231 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(128\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(231, [\chi])\).

	Total	New	Old
Modular forms	200	200	0
Cusp forms	184	184	0
Eisenstein series	16	16	0

Trace form

184 * q - 2 * q^3 - 356 * q^4 + 30 * q^9 + 90 * q^12 - 36 * q^15 - 1076 * q^16 - 84 * q^22 + 2220 * q^25 - 32 * q^27 + 272 * q^31 - 115 * q^33 + 528 * q^34 - 44 * q^36 + 296 * q^37 - 1296 * q^42 - 886 * q^45 - 368 * q^48 + 100 * q^49 - 256 * q^55 - 3504 * q^58 + 228 * q^60 + 3472 * q^64 - 120 * q^66 - 1132 * q^67 + 2204 * q^69 - 3768 * q^70 + 112 * q^75 + 1832 * q^78 - 946 * q^81 - 2748 * q^82 - 918 * q^88 + 4368 * q^91 + 210 * q^93 + 7616 * q^97 - 4178 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(231, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
231.4.l.a	$231$	$4$	231.l	231.l	$6$	$184$	$92$	$13.629$		None		✓	✓	✓	231.4.l.a	$8$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$