Space of modular forms of level 344, weight 1, and Character 344.s

• Label: 344.1.s
• Level: $344$
• Weight: $1$
• Character orbit: 344.s
• Rep. character: $\chi_{344}(11,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $44$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 344 = 2^{3} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	344.s (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 344 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(44\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(344, [\chi])\).

	Total	New	Old
Modular forms	18	18	0
Cusp forms	6	6	0
Eisenstein series	12	12	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(344, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
344.1.s.a	$344$	$1$	344.s	344.s	$14$	$6$	$1$	$0.172$	\(\Q(\zeta_{14})\)	$D_{7}$	\(\Q(\sqrt{-2}) \)	None		✓	✓	✓	344.1.s.a	$4$	$0$	\(-1\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+\zeta_{14}^{2}q^{2}+(-\zeta_{14}+\zeta_{14}^{2})q^{3}+\zeta_{14}^{4}q^{4}+\cdots\)