Space of modular forms of level 231, weight 3, and Character 231.f

• Label: 231.3.f
• Level: $231$
• Weight: $3$
• Character orbit: 231.f
• Rep. character: $\chi_{231}(34,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	231.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(231, [\chi])\).

	Total	New	Old
Modular forms	68	28	40
Cusp forms	60	28	32
Eisenstein series	8	0	8

Trace form

\( 28 q + 64 q^{4} - 8 q^{7} + 24 q^{8} - 84 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(231, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
231.3.f.a	$231$	$3$	231.f	7.b	$2$	$28$	$28$	$6.294$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(231, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(231, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)