Space of modular forms of level 1664, weight 1, and Character 1664.bv

• Label: 1664.1.bv
• Level: $1664$
• Weight: $1$
• Character orbit: 1664.bv
• Rep. character: $\chi_{1664}(193,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1664 = 2^{7} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1664.bv (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1664, [\chi])\).

	Total	New	Old
Modular forms	72	8	64
Cusp forms	8	8	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	8	0	0	0

Trace form

\( 8 q - 4 q^{9} - 8 q^{41} + 8 q^{65} + 4 q^{73} - 4 q^{81} - 4 q^{89} + 4 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1664, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1664.1.bv.a	$1664$	$1$	1664.bv	104.x	$12$	$4$	$1$	$0.830$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-1}) \)	None		✓			1664.1.bv.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{5}-\zeta_{12}^{2}q^{9}-\zeta_{12}q^{13}+\cdots\)
1664.1.bv.b	$1664$	$1$	1664.bv	104.x	$12$	$4$	$1$	$0.830$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-1}) \)	None		✓			1664.1.bv.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+(-\zeta_{12}^{4}-\zeta_{12}^{5})q^{5}-\zeta_{12}^{2}q^{9}+\cdots\)