Space of modular forms of level 109, weight 2, and Character 109.f

• Label: 109.2.f
• Level: $109$
• Weight: $2$
• Character orbit: 109.f
• Rep. character: $\chi_{109}(16,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $42$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	109.f (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 109 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(109, [\chi])\).

	Total	New	Old
Modular forms	54	54	0
Cusp forms	42	42	0
Eisenstein series	12	12	0

Trace form

\( 42 q - 6 q^{3} - 12 q^{4} - 6 q^{5} + 12 q^{6} + 3 q^{7} - 12 q^{8} - 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(109, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
109.2.f.a	$109$	$2$	109.f	109.f	$9$	$42$	$7$	$0.870$		None		$2$	$0$	\(0\)	\(-6\)	\(-6\)	\(3\)		$\mathrm{SU}(2)[C_{9}]$