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

• Label: 353.2.d
• Level: $353$
• Weight: $2$
• Character orbit: 353.d
• Rep. character: $\chi_{353}(70,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $112$
• Newform subspaces: $1$
• Sturm bound: $59$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	353.d (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 353 \)
Character field:			\(\Q(\zeta_{8})\)
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	120	120	0
Cusp forms	112	112	0
Eisenstein series	8	8	0

Trace form

\( 112 q - 112 q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{7} + 4 q^{9} + O(q^{10}) \)

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	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
353.2.d.a	$353$	$2$	353.d	353.d	$8$	$112$	$28$	$2.819$		None		✓	353.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)		$\mathrm{SU}(2)[C_{8}]$