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

• Label: 353.2.j
• Level: $353$
• Weight: $2$
• Character orbit: 353.j
• Rep. character: $\chi_{353}(2,\cdot)$
• Character field: $\Q(\zeta_{88})$
• Dimension: $1120$
• Newform subspaces: $1$
• Sturm bound: $59$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	353.j (of order \(88\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 353 \)
Character field:			\(\Q(\zeta_{88})\)
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	1200	1200	0
Cusp forms	1120	1120	0
Eisenstein series	80	80	0

Trace form

\( 1120 q - 44 q^{2} - 44 q^{3} + 68 q^{4} - 40 q^{5} - 52 q^{6} - 40 q^{7} - 44 q^{8} - 48 q^{9} + O(q^{10}) \)

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.j.a	$353$	$2$	353.j	353.j	$88$	$1120$	$28$	$2.819$		None		$2$	$0$	\(-44\)	\(-44\)	\(-40\)	\(-40\)		$\mathrm{SU}(2)[C_{88}]$