Space of modular forms of level 171, weight 2, and Character 171.t

• Label: 171.2.t
• Level: $171$
• Weight: $2$
• Character orbit: 171.t
• Rep. character: $\chi_{171}(122,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(171, [\chi])\).

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

Trace form

36 * q - 6 * q^2 - 3 * q^3 + 30 * q^4 - 3 * q^5 - 11 * q^6 - q^7 - 12 * q^8 + 5 * q^9 - 6 * q^10 - 9 * q^11 - 15 * q^12 - 3 * q^14 + 18 * q^15 + 18 * q^16 + 27 * q^17 - 6 * q^18 + q^19 + 9 * q^20 + 6 * q^21 - 6 * q^22 - 5 * q^24 + 11 * q^25 - 9 * q^27 + 2 * q^28 - 12 * q^29 - 35 * q^30 - 12 * q^31 - 30 * q^32 - 21 * q^33 - 21 * q^34 - 15 * q^35 - 3 * q^36 - 36 * q^38 - 14 * q^39 - 30 * q^40 + 18 * q^41 - 26 * q^42 - 6 * q^43 - 66 * q^44 + 29 * q^45 + 45 * q^47 - 21 * q^48 - 9 * q^49 - 3 * q^50 - 36 * q^51 + 12 * q^53 + 38 * q^54 - 7 * q^55 - 6 * q^56 + 17 * q^57 - 6 * q^58 - 9 * q^59 + 75 * q^60 + 8 * q^61 + 12 * q^62 + 41 * q^63 + 12 * q^64 + 18 * q^65 + 11 * q^66 + 60 * q^68 + 51 * q^69 - 24 * q^70 - 9 * q^71 - 81 * q^72 - 18 * q^73 + 10 * q^76 - 6 * q^77 - 18 * q^78 + 12 * q^80 + 13 * q^81 - 9 * q^82 - 9 * q^83 + 96 * q^84 - 22 * q^85 + 102 * q^86 - 19 * q^87 - 3 * q^88 + 18 * q^89 + 15 * q^90 + 27 * q^91 + 17 * q^93 - 12 * q^94 - 21 * q^95 - 9 * q^96 + 84 * q^98 - 5 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(171, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
171.2.t.a	$171$	$2$	171.t	171.t	$6$	$36$	$18$	$1.365$		None		✓	✓	✓	171.2.k.a	$2$	$0$	\(-6\)	\(-3\)	\(-3\)	\(-1\)		$\mathrm{SU}(2)[C_{6}]$