Space of modular forms of level 229, weight 1, and Character 229.d

• Label: 229.1.d
• Level: $229$
• Weight: $1$
• Character orbit: 229.d
• Rep. character: $\chi_{229}(107,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $19$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 229 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	229.d (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 229 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(19\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(229, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	4	4	0
Eisenstein series	2	2	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	4	0

Trace form

\( 4 q + 2 q^{2} - 2 q^{6} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(229, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
229.1.d.a	$229$	$1$	229.d	229.d	$4$	$2$	$1$	$0.114$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)	$1$		\(q+q^{3}+iq^{4}-iq^{5}+(-1-i)q^{7}+\cdots\)
229.1.d.b	$229$	$1$	229.d	229.d	$4$	$2$	$1$	$0.114$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		$2$	$0$	\(2\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+(1-i)q^{2}-q^{3}-iq^{4}-iq^{5}+(-1+\cdots)q^{6}+\cdots\)