Space of modular forms of level 153, weight 2, and Character 153.s

• Label: 153.2.s
• Level: $153$
• Weight: $2$
• Character orbit: 153.s
• Rep. character: $\chi_{153}(5,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $256$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 153 \)
Character field:			\(\Q(\zeta_{48})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(153, [\chi])\).

	Total	New	Old
Modular forms	320	320	0
Cusp forms	256	256	0
Eisenstein series	64	64	0

Trace form

\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(153, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
153.2.s.a	$153$	$2$	153.s	153.s	$48$	$256$	$16$	$1.222$		None		$4$	$0$	\(-24\)	\(-16\)	\(-24\)	\(-8\)		$\mathrm{SU}(2)[C_{48}]$