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

• Label: 344.1.b
• Level: $344$
• Weight: $1$
• Character orbit: 344.b
• Rep. character: $\chi_{344}(257,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 43 \)
Character field:			\(\Q\)
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	8	2	6
Cusp forms	4	2	2
Eisenstein series	4	0	4

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	2	0

Trace form

\( 2 q - 2 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
344.1.b.a	$344$	$1$	344.b	43.b	$2$	$2$	$2$	$0.172$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{3}-\beta q^{5}+\beta q^{7}-q^{9}-q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(344, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(344, [\chi]) \cong \)