Space of modular forms of level 344, weight 2, and Character 344.z

• Label: 344.2.z
• Level: $344$
• Weight: $2$
• Character orbit: 344.z
• Rep. character: $\chi_{344}(13,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $504$
• Newform subspaces: $1$
• Sturm bound: $88$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 344 = 2^{3} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	344.z (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 344 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(88\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(344, [\chi])\).

	Total	New	Old
Modular forms	552	552	0
Cusp forms	504	504	0
Eisenstein series	48	48	0

Trace form

\( 504 q - 8 q^{2} - 12 q^{4} - 8 q^{6} - 36 q^{7} - 14 q^{8} - 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(344, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
344.2.z.a	$344$	$2$	344.z	344.z	$42$	$504$	$42$	$2.747$		None		✓	✓	✓	344.2.z.a	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(-36\)		$\mathrm{SU}(2)[C_{42}]$