Space of modular forms of level 29, weight 9, and Character 29.c

• Label: 29.9.c
• Level: $29$
• Weight: $9$
• Character orbit: 29.c
• Rep. character: $\chi_{29}(12,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $38$
• Newform subspaces: $1$
• Sturm bound: $22$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(22\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(29, [\chi])\).

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

Trace form

\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(29, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
29.9.c.a	$29$	$9$	29.c	29.c	$4$	$38$	$19$	$11.814$		None		$2$	$0$	\(-8\)	\(-2\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$