Space of modular forms of level 1792, weight 1, and Character 1792.bt

• Label: 1792.1.bt
• Level: $1792$
• Weight: $1$
• Character orbit: 1792.bt
• Rep. character: $\chi_{1792}(13,\cdot)$
• Character field: $\Q(\zeta_{64})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $256$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1792.bt (of order \(64\) and degree \(32\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1792 \)
Character field:			\(\Q(\zeta_{64})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(256\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1792, [\chi])\).

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

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

\( 32 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1792, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1792.1.bt.a	$1792$	$1$	1792.bt	1792.at	$64$	$32$	$1$	$0.894$	\(\Q(\zeta_{64})\)	$D_{64}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{64}^{3}q^{2}+\zeta_{64}^{6}q^{4}-\zeta_{64}^{7}q^{7}+\cdots\)