Space of modular forms of level 736, weight 1, and Character 736.p

• Label: 736.1.p
• Level: $736$
• Weight: $1$
• Character orbit: 736.p
• Rep. character: $\chi_{736}(45,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 736 = 2^{5} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	736.p (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 736 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(736, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	12	12	0
Eisenstein series	8	8	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q - 12 q^{27} - 12 q^{36} - 12 q^{39} + 12 q^{58} - 12 q^{62} + 12 q^{72} + 12 q^{78}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(736, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
736.1.p.a	$736$	$1$	736.p	736.p	$8$	$4$	$1$	$0.367$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-23}) \)	None		✓			736.1.p.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}q^{2}+(-1+\zeta_{8})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
736.1.p.b	$736$	$1$	736.p	736.p	$8$	$8$	$2$	$0.367$	\(\Q(\zeta_{24})\)	$D_{24}$	\(\Q(\sqrt{-23}) \)	None		✓	✓		736.1.p.b	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{5}q^{2}+(\zeta_{24}-\zeta_{24}^{8})q^{3}+\zeta_{24}^{10}q^{4}+\cdots\)