Space of modular forms of level 3963, weight 1, and Character 3963.bi

• Label: 3963.1.bi
• Level: $3963$
• Weight: $1$
• Character orbit: 3963.bi
• Rep. character: $\chi_{3963}(71,\cdot)$
• Character field: $\Q(\zeta_{44})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $440$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3963 = 3 \cdot 1321 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3963.bi (of order \(44\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3963 \)
Character field:			\(\Q(\zeta_{44})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(440\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3963, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	20	20	0
Eisenstein series	40	40	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q + 2 q^{3} - 20 q^{4} - 2 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3963, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3963.1.bi.a	$3963$	$1$	3963.bi	3963.ai	$44$	$20$	$1$	$1.978$	\(\Q(\zeta_{44})\)	$D_{44}$	\(\Q(\sqrt{-3}) \)	None		✓	3963.1.bi.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{44}^{20}q^{3}-q^{4}+(-\zeta_{44}^{2}-\zeta_{44}^{15}+\cdots)q^{7}+\cdots\)