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	$8$	$0$	$4$	$0$	$0$	$0$	$1$		$q-\zeta_{40}^{16}q^{2}-\zeta_{40}^{12}q^{4}-\zeta_{40}^{14}q^{5}+\cdots$