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

• Label: 171.4.e
• Level: $171$
• Weight: $4$
• Character orbit: 171.e
• Rep. character: $\chi_{171}(58,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $108$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	124	108	16
Cusp forms	116	108	8
Eisenstein series	8	0	8

Trace form

\( 108 q + 4 q^{3} - 216 q^{4} + 28 q^{5} + 14 q^{6} - 12 q^{8} - 124 q^{9} + O(q^{10}) \)

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.e.a	$171$	$4$	171.e	9.c	$3$	$54$	$27$	$10.089$		None		✓			171.4.e.a	$2$	$0$	\(-6\)	\(2\)	\(-26\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$
171.4.e.b	$171$	$4$	171.e	9.c	$3$	$54$	$27$	$10.089$		None		✓			171.4.e.b	$2$	$0$	\(6\)	\(2\)	\(54\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{4}^{\mathrm{old}}(171, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)