Space of modular forms of level 2944, weight 1, and Character 2944.bf

• Label: 2944.1.bf
• Level: $2944$
• Weight: $1$
• Character orbit: 2944.bf
• Rep. character: $\chi_{2944}(45,\cdot)$
• Character field: $\Q(\zeta_{32})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2944 = 2^{7} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2944.bf (of order \(32\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2944 \)
Character field:			\(\Q(\zeta_{32})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2944, [\chi])\).

	Total	New	Old
Modular forms	80	80	0
Cusp forms	48	48	0
Eisenstein series	32	32	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	48	0	0	0

Trace form

\( 48 q - 48 q^{58} - 48 q^{72}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2944, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2944.1.bf.a	$2944$	$1$	2944.bf	2944.af	$32$	$16$	$1$	$1.469$	\(\Q(\zeta_{32})\)	$D_{32}$	\(\Q(\sqrt{-23}) \)	None		✓			2944.1.bf.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{32}^{11}q^{2}+(-\zeta_{32}^{4}-\zeta_{32}^{11})q^{3}+\cdots\)
2944.1.bf.b	$2944$	$1$	2944.bf	2944.af	$32$	$32$	$2$	$1.469$	\(\Q(\zeta_{96})\)	$D_{96}$	\(\Q(\sqrt{-23}) \)	None		✓	✓		2944.1.bf.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{96}^{5}q^{2}+(-\zeta_{96}^{37}+\zeta_{96}^{44})q^{3}+\cdots\)