Space of modular forms of level 728, weight 2, and Character 728.bf

• Label: 728.2.bf
• Level: $728$
• Weight: $2$
• Character orbit: 728.bf
• Rep. character: $\chi_{728}(3,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $216$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.bf (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 728 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(728, [\chi])\).

	Total	New	Old
Modular forms	232	232	0
Cusp forms	216	216	0
Eisenstein series	16	16	0

Trace form

\( 216 q + q^{2} + q^{4} + 12 q^{6} - 8 q^{8} - 204 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(728, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
728.2.bf.a	$728$	$2$	728.bf	728.af	$6$	$4$	$2$	$5.813$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1-2\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
728.2.bf.b	$728$	$2$	728.bf	728.af	$6$	$212$	$106$	$5.813$		None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$