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

• Label: 731.2.m
• Level: $731$
• Weight: $2$
• Character orbit: 731.m
• Rep. character: $\chi_{731}(87,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $248$
• Newform subspaces: $3$
• Sturm bound: $132$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(132\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	272	248	24
Cusp forms	256	248	8
Eisenstein series	16	0	16

Trace form

\( 248 q - 16 q^{6} + O(q^{10}) \)

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.m.a	$731$	$2$	731.m	17.d	$8$	$4$	$1$	$5.837$	\(\Q(\zeta_{8})\)	None		$2$	$1$	\(-4\)	\(-4\)	\(-8\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
731.2.m.b	$731$	$2$	731.m	17.d	$8$	$116$	$29$	$5.837$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
731.2.m.c	$731$	$2$	731.m	17.d	$8$	$128$	$32$	$5.837$		None		$2$	$0$	\(4\)	\(4\)	\(8\)	\(4\)		$\mathrm{SU}(2)[C_{8}]$

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

\( S_{2}^{\mathrm{old}}(731, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)