Space of modular forms of level 1984, weight 1, and Character 1984.bn

• Label: 1984.1.bn
• Level: $1984$
• Weight: $1$
• Character orbit: 1984.bn
• Rep. character: $\chi_{1984}(61,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $256$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1984 = 2^{6} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1984.bn (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1984 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(256\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1984, [\chi])\).

	Total	New	Old
Modular forms	40	40	0
Cusp forms	24	24	0
Eisenstein series	16	16	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1984, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1984.1.bn.a	$1984$	$1$	1984.bn	1984.an	$16$	$8$	$1$	$0.990$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-31}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$		\(q-\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}+(-1-\zeta_{16}+\cdots)q^{5}+\cdots\)
1984.1.bn.b	$1984$	$1$	1984.bn	1984.an	$16$	$16$	$2$	$0.990$	\(\Q(\zeta_{48})\)	$D_{48}$	\(\Q(\sqrt{-31}) \)	None		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$		\(q+\zeta_{48}^{14}q^{2}-\zeta_{48}^{4}q^{4}+(-\zeta_{48}^{16}+\cdots)q^{5}+\cdots\)