Space of modular forms of level 964, weight 1, and Character 964.bh

• Label: 964.1.bh
• Level: $964$
• Weight: $1$
• Character orbit: 964.bh
• Rep. character: $\chi_{964}(83,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $121$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 964 = 2^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	964.bh (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 964 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(121\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(964, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	16	16	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	16	0	0	0

Trace form

\( 16 q + 8 q^{4} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(964, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
964.1.bh.a	$964$	$1$	964.bh	964.ah	$60$	$16$	$1$	$0.481$	\(\Q(\zeta_{60})\)	$D_{60}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{60}^{5}q^{2}+\zeta_{60}^{10}q^{4}+(-\zeta_{60}+\zeta_{60}^{23}+\cdots)q^{5}+\cdots\)