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

• Label: 1792.1.o
• Level: $1792$
• Weight: $1$
• Character orbit: 1792.o
• Rep. character: $\chi_{1792}(639,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $256$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1792.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(256\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	56	16	40
Cusp forms	8	8	0
Eisenstein series	48	8	40

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	8	0	0

Trace form

\( 8 q + O(q^{10}) \)

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.o.a	$1792$	$1$	1792.o	56.k	$6$	$4$	$2$	$0.894$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1792.1.o.b	$1792$	$1$	1792.o	56.k	$6$	$4$	$2$	$0.894$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)