Space of modular forms of level 211, weight 2, and Character 211.o

• Label: 211.2.o
• Level: $211$
• Weight: $2$
• Character orbit: 211.o
• Rep. character: $\chi_{211}(4,\cdot)$
• Character field: $\Q(\zeta_{105})$
• Dimension: $816$
• Newform subspaces: $1$
• Sturm bound: $35$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	211.o (of order \(105\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 211 \)
Character field:			\(\Q(\zeta_{105})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(35\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(211, [\chi])\).

	Total	New	Old
Modular forms	912	912	0
Cusp forms	816	816	0
Eisenstein series	96	96	0

Trace form

\( 816 q - 51 q^{2} - 49 q^{3} - 71 q^{4} - 50 q^{5} - 51 q^{6} - 54 q^{7} - 51 q^{8} - 54 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(211, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
211.2.o.a	$211$	$2$	211.o	211.o	$105$	$816$	$17$	$1.685$		None		$2$	$0$	\(-51\)	\(-49\)	\(-50\)	\(-54\)		$\mathrm{SU}(2)[C_{105}]$