Space of modular forms of level 152, weight 3, and Character 152.s

• Label: 152.3.s
• Level: $152$
• Weight: $3$
• Character orbit: 152.s
• Rep. character: $\chi_{152}(13,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $228$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	152.s (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(152, [\chi])\).

	Total	New	Old
Modular forms	252	252	0
Cusp forms	228	228	0
Eisenstein series	24	24	0

Trace form

\( 228 q - 6 q^{2} - 12 q^{4} + 12 q^{6} - 6 q^{7} - 9 q^{8} - 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.3.s.a	$152$	$3$	152.s	152.s	$18$	$228$	$38$	$4.142$		None		$4$	$0$	\(-6\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$