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

• Label: 169.2.b
• Level: $169$
• Weight: $2$
• Character orbit: 169.b
• Rep. character: $\chi_{169}(168,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	22	18	4
Cusp forms	8	8	0
Eisenstein series	14	10	4

Trace form

\( 8 q - 2 q^{4} - 4 q^{9} + O(q^{10}) \)

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.b.a	$169$	$2$	169.b	13.b	$2$	$2$	$2$	$1.349$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}+2q^{3}-q^{4}+\zeta_{6}q^{5}-2\zeta_{6}q^{6}+\cdots\)
169.2.b.b	$169$	$2$	169.b	13.b	$2$	$6$	$6$	$1.349$	6.0.153664.1	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{5})q^{2}+(-1+\beta _{4})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots\)