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

• Label: 211.3.m
• Level: $211$
• Weight: $3$
• Character orbit: 211.m
• Rep. character: $\chi_{211}(26,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $408$
• Newform subspaces: $1$
• Sturm bound: $53$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	211.m (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 211 \)
Character field:			\(\Q(\zeta_{42})\)
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	432	432	0
Cusp forms	408	408	0
Eisenstein series	24	24	0

Trace form

\( 408 q - 4 q^{2} - 14 q^{3} - 90 q^{4} - 10 q^{5} + 29 q^{6} + 10 q^{7} + 56 q^{8} - 96 q^{9} + O(q^{10}) \)

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	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
211.3.m.a	$211$	$3$	211.m	211.m	$42$	$408$	$34$	$5.749$		None		✓	211.3.m.a	$2$	$0$	\(-4\)	\(-14\)	\(-10\)	\(10\)		$\mathrm{SU}(2)[C_{42}]$