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

• Label: 169.2.c
• Level: $169$
• Weight: $2$
• Character orbit: 169.c
• Rep. character: $\chi_{169}(22,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $30$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(30\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	44	36	8
Cusp forms	16	16	0
Eisenstein series	28	20	8

Trace form

\( 16 q - 2 q^{4} + 4 q^{9} + O(q^{10}) \)

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.c.a	$169$	$2$	169.c	13.c	$3$	$4$	$2$	$1.349$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{12}^{2}q^{2}-2\zeta_{12}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots\)
169.2.c.b	$169$	$2$	169.c	13.c	$3$	$6$	$3$	$1.349$	6.0.64827.1	None		$2$	$0$	\(-2\)	\(2\)	\(8\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{4}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{5})q^{3}+\cdots\)
169.2.c.c	$169$	$2$	169.c	13.c	$3$	$6$	$3$	$1.349$	6.0.64827.1	None		$2$	$0$	\(2\)	\(2\)	\(-8\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{4})q^{2}+(1-\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)