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

• Label: 169.2.e
• Level: $169$
• Weight: $2$
• Character orbit: 169.e
• Rep. character: $\chi_{169}(23,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
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	46	34	12
Cusp forms	18	14	4
Eisenstein series	28	20	8

Trace form

\( 14 q + 3 q^{2} + 2 q^{3} + q^{4} - 6 q^{6} + 5 q^{9} + O(q^{10}) \)

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.e.a	$169$	$2$	169.e	13.e	$6$	$2$	$1$	$1.349$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(3\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
169.2.e.b	$169$	$2$	169.e	13.e	$6$	$12$	$6$	$1.349$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{8}+\beta _{10})q^{2}+(1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(169, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(169, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)