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

• Label: 231.4.e
• Level: $231$
• Weight: $4$
• Character orbit: 231.e
• Rep. character: $\chi_{231}(188,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• 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.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
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	80	20
Cusp forms	92	80	12
Eisenstein series	8	0	8

Trace form

80 * q - 320 * q^4 - 8 * q^7 - 56 * q^9 + 256 * q^15 + 1280 * q^16 - 156 * q^18 + 56 * q^21 + 2000 * q^25 + 416 * q^28 + 44 * q^30 + 1152 * q^36 - 1456 * q^37 - 1328 * q^39 - 1536 * q^42 - 1096 * q^43 + 1416 * q^46 + 1088 * q^49 + 2176 * q^51 + 2360 * q^57 - 1620 * q^58 - 4964 * q^60 - 2460 * q^63 - 4652 * q^64 + 1384 * q^67 + 6012 * q^70 - 2616 * q^72 + 8204 * q^78 + 448 * q^79 - 5608 * q^81 - 3404 * q^84 - 1344 * q^85 + 396 * q^88 - 2904 * q^91 + 4104 * q^93

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.e.a	$231$	$4$	231.e	21.c	$2$	$80$	$80$	$13.629$		None		✓	✓	✓	231.4.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{4}^{\mathrm{old}}(231, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)