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

• Label: 229.2.e
• Level: $229$
• Weight: $2$
• Character orbit: 229.e
• Rep. character: $\chi_{229}(95,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $38$
• Newform subspaces: $2$
• Sturm bound: $38$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	229.e (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 229 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(38\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	42	42	0
Cusp forms	38	38	0
Eisenstein series	4	4	0

Trace form

\( 38 q - q^{3} - 52 q^{4} + 3 q^{6} - 26 q^{9} + O(q^{10}) \)

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.e.a	$229$	$2$	229.e	229.e	$6$	$2$	$1$	$1.829$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-q^{4}-3\zeta_{6}q^{5}+\cdots\)
229.2.e.b	$229$	$2$	229.e	229.e	$6$	$36$	$18$	$1.829$		None		$2$	$0$	\(0\)	\(-2\)	\(3\)	\(3\)		$\mathrm{SU}(2)[C_{6}]$