Space of modular forms of level 171, weight 4, and Character 171.y

• Label: 171.4.y
• Level: $171$
• Weight: $4$
• Character orbit: 171.y
• Rep. character: $\chi_{171}(53,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $120$
• Newform subspaces: $1$
• Sturm bound: $80$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.y (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(80\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(171, [\chi])\).

	Total	New	Old
Modular forms	384	120	264
Cusp forms	336	120	216
Eisenstein series	48	0	48

Trace form

120 * q - 36 * q^4 - 180 * q^10 - 156 * q^13 + 180 * q^16 + 924 * q^19 + 432 * q^22 - 360 * q^25 - 624 * q^28 + 324 * q^34 + 1440 * q^40 + 1524 * q^43 + 3888 * q^46 - 3228 * q^49 - 6000 * q^52 - 4464 * q^55 + 5616 * q^58 - 5736 * q^61 - 4524 * q^64 + 372 * q^67 + 7848 * q^70 - 276 * q^73 + 4320 * q^76 + 10536 * q^79 + 3960 * q^82 - 11592 * q^85 - 11664 * q^88 - 120 * q^91 + 5904 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(171, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
171.4.y.a	$171$	$4$	171.y	57.j	$18$	$120$	$20$	$10.089$		None		✓	✓	✓	171.4.y.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{4}^{\mathrm{old}}(171, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(171, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)