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

• Label: 155.3.o
• Level: $155$
• Weight: $3$
• Character orbit: 155.o
• Rep. character: $\chi_{155}(67,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $120$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	155.o (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{12})\)
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	136	136	0
Cusp forms	120	120	0
Eisenstein series	16	16	0

Trace form

\( 120 q - 8 q^{2} - 6 q^{3} - 2 q^{5} + 8 q^{6} + 6 q^{7} + 36 q^{8} + O(q^{10}) \)

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	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
155.3.o.a	$155$	$3$	155.o	155.o	$12$	$120$	$30$	$4.223$		None		✓	✓	✓	155.3.o.a	$4$	$0$	\(-8\)	\(-6\)	\(-2\)	\(6\)		$\mathrm{SU}(2)[C_{12}]$