Space of modular forms of level 211, weight 3, and Character 211.e

• Label: 211.3.e
• Level: $211$
• Weight: $3$
• Character orbit: 211.e
• Rep. character: $\chi_{211}(15,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $68$
• Newform subspaces: $1$
• Sturm bound: $53$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	211.e (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 211 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(53\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(211, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	68	68	0
Eisenstein series	4	4	0

Trace form

\( 68 q - 3 q^{2} + 55 q^{4} - 4 q^{5} - q^{6} - 24 q^{7} + 82 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(211, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
211.3.e.a	$211$	$3$	211.e	211.e	$6$	$68$	$34$	$5.749$		None		$2$	$0$	\(-3\)	\(0\)	\(-4\)	\(-24\)		$\mathrm{SU}(2)[C_{6}]$