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

• Label: 3960.1.eg
• Level: $3960$
• Weight: $1$
• Character orbit: 3960.eg
• Rep. character: $\chi_{3960}(899,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $864$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3960.eg (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1320 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(864\)
Trace bound:			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	96	32	64
Cusp forms	32	32	0
Eisenstein series	64	0	64

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

\( 32 q - 8 q^{4} - 8 q^{16} + 8 q^{25} + 8 q^{49} - 8 q^{64} - 16 q^{91} + 40 q^{94}+O(q^{100}) \)

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.eg.a	$3960$	$1$	3960.eg	1320.ca	$10$	$16$	$4$	$1.976$	\(\Q(\zeta_{40})\)	$D_{20}$	\(\Q(\sqrt{-10}) \)	None		✓			3960.1.eg.a	$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{40}^{16}q^{2}-\zeta_{40}^{12}q^{4}+\zeta_{40}^{14}q^{5}+\cdots\)
3960.1.eg.b	$3960$	$1$	3960.eg	1320.ca	$10$	$16$	$4$	$1.976$	\(\Q(\zeta_{40})\)	$D_{20}$	\(\Q(\sqrt{-10}) \)	None		✓			3960.1.eg.a	$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{40}^{16}q^{2}-\zeta_{40}^{12}q^{4}-\zeta_{40}^{14}q^{5}+\cdots\)