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 + 7 * q^10 - 4 * q^12 - 20 * q^14 - 6 * q^15 + q^16 - q^17 + 6 * q^19 - 3 * q^20 - 6 * q^22 - 4 * q^23 + 6 * q^24 + 24 * q^25 - 4 * q^27 - q^29 - 8 * q^30 + 9 * q^32 - 8 * q^35 - 13 * q^36 - 15 * q^37 - 36 * q^38 - 6 * q^40 + 9 * q^41 - 16 * q^42 + 18 * q^43 + 3 * q^45 + 18 * q^46 + 8 * q^48 - 15 * q^49 + 6 * q^50 - 8 * q^51 - 2 * q^53 - 12 * q^54 - 12 * q^55 - 8 * q^56 - 9 * q^58 - 12 * q^59 - 9 * q^61 + 8 * q^62 + 42 * q^64 + 20 * q^66 - 6 * q^67 + 39 * q^68 - 6 * q^71 - 3 * q^72 + q^74 + 26 * q^75 + 6 * q^76 - 32 * q^77 - 12 * q^79 + 15 * q^80 + 13 * q^81 - 19 * q^82 - 9 * q^85 + 30 * q^87 + 30 * q^88 + 12 * q^89 + 54 * q^90 + 12 * q^92 + 12 * q^93 - 16 * q^94 + 12 * q^95 - 12 * q^97 - 21 * q^98

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.e.a	$169$	$2$	169.e	13.e	$6$	$2$	$1$	$1.349$	\(\Q(\sqrt{-3}) \)	None					13.2.e.a	$2$	$0$	\(3\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
169.2.e.b	$169$	$2$	169.e	13.e	$6$	$12$	$6$	$1.349$	12.0.\(\cdots\).1	None		✓	✓		169.2.a.b	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{8}+\beta _{10})q^{2}+(1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)

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

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