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

• Label: 231.4.c
• Level: $231$
• Weight: $4$
• Character orbit: 231.c
• Rep. character: $\chi_{231}(76,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• 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.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
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	48	52
Cusp forms	92	48	44
Eisenstein series	8	0	8

Trace form

48 * q - 172 * q^4 - 432 * q^9 + 20 * q^11 + 40 * q^14 - 168 * q^15 + 660 * q^16 + 492 * q^22 - 552 * q^23 - 320 * q^25 + 1548 * q^36 + 704 * q^37 + 900 * q^42 - 736 * q^44 - 416 * q^49 - 2880 * q^53 - 968 * q^56 + 1580 * q^58 + 1404 * q^60 - 7744 * q^64 + 2456 * q^67 - 2508 * q^70 - 312 * q^71 + 2952 * q^77 + 3492 * q^78 + 3888 * q^81 + 11344 * q^86 - 2880 * q^88 - 1760 * q^91 + 7808 * q^92 + 2712 * q^93 - 180 * 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.c.a	$231$	$4$	231.c	77.b	$2$	$48$	$48$	$13.629$		None		✓	✓	✓	231.4.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{4}^{\mathrm{old}}(231, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)