Space of modular forms of level 169, weight 2, and Character 169.i

• Label: 169.2.i
• Level: $169$
• Weight: $2$
• Character orbit: 169.i
• Rep. character: $\chi_{169}(3,\cdot)$
• Character field: $\Q(\zeta_{39})$
• Dimension: $336$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.i (of order \(39\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{39})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(169, [\chi])\).

	Total	New	Old
Modular forms	384	384	0
Cusp forms	336	336	0
Eisenstein series	48	48	0

Trace form

\( 336 q - 26 q^{2} - 26 q^{3} - 12 q^{4} - 26 q^{5} - 26 q^{6} - 26 q^{7} - 26 q^{8} - 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(169, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
169.2.i.a	$169$	$2$	169.i	169.i	$39$	$336$	$14$	$1.349$		None		$2$	$0$	\(-26\)	\(-26\)	\(-26\)	\(-26\)		$\mathrm{SU}(2)[C_{39}]$