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

• Label: 109.2.i
• Level: $109$
• Weight: $2$
• Character orbit: 109.i
• Rep. character: $\chi_{109}(3,\cdot)$
• Character field: $\Q(\zeta_{27})$
• Dimension: $144$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	109.i (of order \(27\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 109 \)
Character field:			\(\Q(\zeta_{27})\)
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	180	180	0
Cusp forms	144	144	0
Eisenstein series	36	36	0

Trace form

\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} + 18 q^{8} + O(q^{10}) \)

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.i.a	$109$	$2$	109.i	109.i	$27$	$144$	$8$	$0.870$		None		$2$	$0$	\(-18\)	\(-18\)	\(-18\)	\(-18\)		$\mathrm{SU}(2)[C_{27}]$