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

• Label: 731.2.e
• Level: $731$
• Weight: $2$
• Character orbit: 731.e
• Rep. character: $\chi_{731}(307,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $116$
• Newform subspaces: $2$
• Sturm bound: $132$
• Trace bound: $2$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	136	116	20
Cusp forms	128	116	12
Eisenstein series	8	0	8

Trace form

\( 116 q - 4 q^{2} - 2 q^{3} + 108 q^{4} - 4 q^{5} + 4 q^{6} - 6 q^{7} - 52 q^{9} + O(q^{10}) \)

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.e.a	$731$	$2$	731.e	43.c	$3$	$58$	$29$	$5.837$		None		$2$	$0$	\(-6\)	\(3\)	\(-1\)	\(7\)		$\mathrm{SU}(2)[C_{3}]$
731.2.e.b	$731$	$2$	731.e	43.c	$3$	$58$	$29$	$5.837$		None		$2$	$0$	\(2\)	\(-5\)	\(-3\)	\(-13\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(731, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(731, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 2}\)