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

• Label: 231.4.g
• Level: $231$
• Weight: $4$
• Character orbit: 231.g
• Rep. character: $\chi_{231}(197,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• 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.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
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	100	72	28
Cusp forms	92	72	20
Eisenstein series	8	0	8

Trace form

72 * q + 288 * q^4 + 4 * q^9 + 16 * q^12 + 20 * q^15 + 1248 * q^16 + 384 * q^22 - 1824 * q^25 - 900 * q^27 + 264 * q^31 - 964 * q^33 - 1008 * q^34 + 48 * q^36 - 24 * q^37 + 1524 * q^45 + 192 * q^48 - 3528 * q^49 + 1728 * q^55 - 3612 * q^58 - 3172 * q^60 + 5844 * q^64 - 2748 * q^66 + 624 * q^67 + 804 * q^69 - 756 * q^70 - 4516 * q^75 - 1268 * q^78 + 4796 * q^81 + 10056 * q^82 + 7428 * q^88 - 1008 * q^91 - 3916 * q^93 + 168 * q^97 - 1260 * 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.g.a	$231$	$4$	231.g	33.d	$2$	$72$	$72$	$13.629$		None		✓	✓	✓	231.4.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(231, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(231, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)