Space of modular forms of level 43, weight 9, and Character 43.f

• Label: 43.9.f
• Level: $43$
• Weight: $9$
• Character orbit: 43.f
• Rep. character: $\chi_{43}(2,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $174$
• Newform subspaces: $1$
• Sturm bound: $33$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	43.f (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 43 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(33\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(43, [\chi])\).

	Total	New	Old
Modular forms	186	186	0
Cusp forms	174	174	0
Eisenstein series	12	12	0

Trace form

\( 174 q - 7 q^{2} - 7 q^{3} + 4021 q^{4} - 7 q^{5} + 1780 q^{6} - 5383 q^{8} + 56490 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(43, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
43.9.f.a	$43$	$9$	43.f	43.f	$14$	$174$	$29$	$17.517$		None		$2$	$0$	\(-7\)	\(-7\)	\(-7\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$