Space of modular forms of level 731, weight 2, and Character 731.f

• Label: 731.2.f
• Level: $731$
• Weight: $2$
• Character orbit: 731.f
• Rep. character: $\chi_{731}(259,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $128$
• Newform subspaces: $4$
• Sturm bound: $132$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(132\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(731, [\chi])\).

	Total	New	Old
Modular forms	136	128	8
Cusp forms	128	128	0
Eisenstein series	8	0	8

Trace form

\( 128 q - 132 q^{4} - 8 q^{5} + 8 q^{6} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(731, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
731.2.f.a	$731$	$2$	731.f	17.c	$4$	$2$	$1$	$5.837$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-iq^{2}+q^{4}+(-1-i)q^{5}+(-2+2i)q^{7}+\cdots\)
731.2.f.b	$731$	$2$	731.f	17.c	$4$	$2$	$1$	$5.837$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+iq^{2}+(2+2i)q^{3}+q^{4}+(-2+2i)q^{6}+\cdots\)
731.2.f.c	$731$	$2$	731.f	17.c	$4$	$56$	$28$	$5.837$		None		$2$	$0$	\(0\)	\(-4\)	\(-2\)	\(4\)		$\mathrm{SU}(2)[C_{4}]$
731.2.f.d	$731$	$2$	731.f	17.c	$4$	$68$	$34$	$5.837$		None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$