Space of modular forms of level 353, weight 2, and Character 353.f

• Label: 353.2.f
• Level: $353$
• Weight: $2$
• Character orbit: 353.f
• Rep. character: $\chi_{353}(36,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $232$
• Newform subspaces: $1$
• Sturm bound: $59$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	353.f (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 353 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(59\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(353, [\chi])\).

	Total	New	Old
Modular forms	248	248	0
Cusp forms	232	232	0
Eisenstein series	16	16	0

Trace form

\( 232 q - 8 q^{2} - 8 q^{3} - 8 q^{5} - 8 q^{6} - 8 q^{7} + 8 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(353, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
353.2.f.a	$353$	$2$	353.f	353.f	$16$	$232$	$29$	$2.819$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)		$\mathrm{SU}(2)[C_{16}]$