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

• Label: 29.9.f
• Level: $29$
• Weight: $9$
• Character orbit: 29.f
• Rep. character: $\chi_{29}(2,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $228$
• Newform subspaces: $1$
• Sturm bound: $22$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.f (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{28})\)
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	252	252	0
Cusp forms	228	228	0
Eisenstein series	24	24	0

Trace form

\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9} + O(q^{10}) \)

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.f.a	$29$	$9$	29.f	29.f	$28$	$228$	$19$	$11.814$		None		$2$	$0$	\(-6\)	\(-12\)	\(-14\)	\(-10\)		$\mathrm{SU}(2)[C_{28}]$