Space of modular forms of level 155, weight 3, and Character 155.i

• Label: 155.3.i
• Level: $155$
• Weight: $3$
• Character orbit: 155.i
• Rep. character: $\chi_{155}(99,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $60$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	155.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(155, [\chi])\).

	Total	New	Old
Modular forms	68	68	0
Cusp forms	60	60	0
Eisenstein series	8	8	0

Trace form

\( 60 q - 124 q^{4} - 4 q^{5} + 36 q^{6} - 100 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(155, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
155.3.i.a	$155$	$3$	155.i	155.i	$6$	$60$	$30$	$4.223$		None		✓	155.3.i.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$