Space of modular forms of level 3920, weight 1, and Character 3920.bt

• Label: 3920.1.bt
• Level: $3920$
• Weight: $1$
• Character orbit: 3920.bt
• Rep. character: $\chi_{3920}(79,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $6$
• Sturm bound: $672$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3920.bt (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 140 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(672\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3920, [\chi])\).

	Total	New	Old
Modular forms	184	20	164
Cusp forms	88	20	68
Eisenstein series	96	0	96

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

\( 20 q - 2 q^{5} - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3920, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3920.1.bt.a	$3920$	$1$	3920.bt	140.p	$6$	$2$	$1$	$1.956$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{5}) \)		$8$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-\zeta_{6}q^{5}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{25}+q^{29}+\cdots\)
3920.1.bt.b	$3920$	$1$	3920.bt	140.p	$6$	$2$	$1$	$1.956$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{5}) \)		$8$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{6}q^{5}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{25}+q^{29}+\cdots\)
3920.1.bt.c	$3920$	$1$	3920.bt	140.p	$6$	$4$	$2$	$1.956$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-5}) \)	None		$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$3$		\(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{4}q^{5}+(-1+\cdots)q^{9}+\cdots\)
3920.1.bt.d	$3920$	$1$	3920.bt	140.p	$6$	$4$	$2$	$1.956$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-35}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}q^{5}+(-1+\cdots)q^{9}+\cdots\)
3920.1.bt.e	$3920$	$1$	3920.bt	140.p	$6$	$4$	$2$	$1.956$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-35}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}q^{5}+(-1+\cdots)q^{9}+\cdots\)
3920.1.bt.f	$3920$	$1$	3920.bt	140.p	$6$	$4$	$2$	$1.956$	\(\Q(\zeta_{12})\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-35}) \)	\(\Q(\sqrt{35}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{5}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{3}q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3920, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)