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

• Label: 3963.1.x
• Level: $3963$
• Weight: $1$
• Character orbit: 3963.x
• Rep. character: $\chi_{3963}(383,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $440$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3963 = 3 \cdot 1321 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3963.x (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3963 \)
Character field:			\(\Q(\zeta_{22})\)
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	30	30	0
Cusp forms	10	10	0
Eisenstein series	20	20	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	10	0	0	0

Trace form

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

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	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3963.1.x.a	$3963$	$1$	3963.x	3963.x	$22$	$10$	$1$	$1.978$	\(\Q(\zeta_{22})\)	$D_{22}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	3963.1.x.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{22}^{6}q^{3}+q^{4}+(-\zeta_{22}^{5}-\zeta_{22}^{10}+\cdots)q^{7}+\cdots\)