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

• Label: 171.2.h
• Level: $171$
• Weight: $2$
• Character orbit: 171.h
• Rep. character: $\chi_{171}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $36$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

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 + q^3 + 30 * q^4 + q^5 - 7 * q^6 - 3 * q^7 - 24 * q^8 + 5 * q^9 - 6 * q^10 - q^11 - 3 * q^12 + 5 * q^14 - 2 * q^15 + 18 * q^16 - 5 * q^17 + 18 * q^18 - 9 * q^19 - q^20 + 2 * q^21 - 10 * q^23 - 39 * q^24 - 9 * q^25 + 4 * q^26 - 5 * q^27 - 6 * q^28 + 16 * q^29 - 17 * q^30 - 6 * q^31 - 54 * q^32 + 7 * q^33 - 15 * q^34 - 3 * q^35 - 7 * q^36 - 6 * q^37 - 30 * q^38 + 6 * q^40 + 16 * q^41 + 22 * q^42 + 18 * q^43 + 28 * q^44 - 29 * q^45 - 21 * q^47 - 15 * q^48 - 9 * q^49 + q^50 + 14 * q^51 - 30 * q^52 + 14 * q^53 - 40 * q^54 + 3 * q^55 - 18 * q^56 + 57 * q^57 - 6 * q^58 + 29 * q^59 - 31 * q^60 - 6 * q^61 + 50 * q^62 + 33 * q^63 - 36 * q^64 + 42 * q^65 + 31 * q^66 + 6 * q^67 - 4 * q^68 + 3 * q^69 + 24 * q^70 + 21 * q^71 - 21 * q^72 - 4 * q^74 - 100 * q^75 - 24 * q^76 + 32 * q^77 + 8 * q^78 - 22 * q^80 + 53 * q^81 - 3 * q^82 - 5 * q^83 + 18 * q^84 + 18 * q^85 - 66 * q^86 - 21 * q^87 - 15 * q^88 + 40 * q^89 + 127 * q^90 + 15 * q^91 + 34 * q^92 - 3 * q^93 - 6 * q^94 + 23 * q^95 - 5 * q^96 - 24 * q^97 + 14 * q^98 - 25 * 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.h.a	$171$	$2$	171.h	171.h	$3$	$2$	$1$	$1.365$	\(\Q(\sqrt{-3}) \)	None		✓			171.2.g.a	$2$	$0$	\(-2\)	\(0\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}-3\zeta_{6}q^{5}+\cdots\)
171.2.h.b	$171$	$2$	171.h	171.h	$3$	$2$	$1$	$1.365$	\(\Q(\sqrt{-3}) \)	None		✓			171.2.g.b	$2$	$0$	\(-2\)	\(0\)	\(1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\zeta_{6}q^{5}+\cdots\)
171.2.h.c	$171$	$2$	171.h	171.h	$3$	$32$	$16$	$1.365$		None		✓	✓		171.2.g.c	$2$	$0$	\(-2\)	\(1\)	\(3\)	\(1\)		$\mathrm{SU}(2)[C_{3}]$