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 - 4 * q^10 + 8 * q^12 - 20 * q^14 + 6 * q^16 - 2 * q^17 - 6 * q^22 - 2 * q^23 - 28 * q^25 - 12 * q^27 - 4 * q^29 + 14 * q^30 - 8 * q^35 + 12 * q^36 + 24 * q^38 - 16 * q^42 - 10 * q^43 + 18 * q^48 + 22 * q^49 + 20 * q^51 - 8 * q^53 - 12 * q^55 + 8 * q^56 - 10 * q^61 - 14 * q^62 - 40 * q^64 + 20 * q^66 + 36 * q^68 - 12 * q^69 - 14 * q^74 - 22 * q^75 + 32 * q^77 - 4 * q^79 + 24 * q^81 + 10 * q^82 + 24 * q^87 - 30 * q^88 - 60 * q^90 + 24 * q^92 - 22 * q^94 - 18 * q^95

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	Twist minimal	Largest	Maximal	Minimal twist	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					13.2.e.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta_{2} q^{2}-2\beta_1 q^{3}+(\beta_1-1)q^{4}+\cdots\)
169.2.c.b	$169$	$2$	169.c	13.c	$3$	$6$	$3$	$1.349$	6.0.64827.1	None		✓			169.2.a.b	$2$	$0$	\(-2\)	\(2\)	\(8\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{4}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{5})q^{3}+\cdots\)
169.2.c.c	$169$	$2$	169.c	13.c	$3$	$6$	$3$	$1.349$	6.0.64827.1	None		✓			169.2.a.b	$2$	$0$	\(2\)	\(2\)	\(-8\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{4})q^{2}+(1-\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)