Space of modular forms of level 3960, weight 1, and Character 3960.cd

• Label: 3960.1.cd
• Level: $3960$
• Weight: $1$
• Character orbit: 3960.cd
• Rep. character: $\chi_{3960}(769,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $864$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3960.cd (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 495 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(864\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3960, [\chi])\).

	Total	New	Old
Modular forms	72	8	64
Cusp forms	40	8	32
Eisenstein series	32	0	32

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	8	0

Trace form

\( 8 q - 8 q^{9} - 4 q^{11} - 4 q^{15} + 4 q^{25} + 4 q^{31} - 4 q^{49} + 4 q^{59} + 4 q^{69} + 8 q^{71} + 8 q^{81} - 8 q^{89} - 16 q^{91} + 4 q^{99}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3960, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3960.1.cd.a	$3960$	$1$	3960.cd	495.o	$6$	$8$	$4$	$1.976$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		✓	✓	✓	3960.1.cd.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+\zeta_{24}^{6}q^{3}+\zeta_{24}^{10}q^{5}+(-\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3960, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3960, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1980, [\chi])\)\(^{\oplus 2}\)