Space of modular forms of level 229, weight 2, and Character 229.i

• Label: 229.2.i
• Level: $229$
• Weight: $2$
• Character orbit: 229.i
• Rep. character: $\chi_{229}(3,\cdot)$
• Character field: $\Q(\zeta_{57})$
• Dimension: $648$
• Newform subspaces: $1$
• Sturm bound: $38$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	229.i (of order \(57\) and degree \(36\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 229 \)
Character field:			\(\Q(\zeta_{57})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(38\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(229, [\chi])\).

	Total	New	Old
Modular forms	720	720	0
Cusp forms	648	648	0
Eisenstein series	72	72	0

Trace form

\( 648 q - 32 q^{2} - 37 q^{3} - 60 q^{4} - 22 q^{5} - 43 q^{6} - 34 q^{7} - 20 q^{8} - 25 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(229, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
229.2.i.a	$229$	$2$	229.i	229.i	$57$	$648$	$18$	$1.829$		None		$2$	$0$	\(-32\)	\(-37\)	\(-22\)	\(-34\)		$\mathrm{SU}(2)[C_{57}]$