Space of modular forms of level 392, weight 3, and Character 392.r

• Label: 392.3.r
• Level: $392$
• Weight: $3$
• Character orbit: 392.r
• Rep. character: $\chi_{392}(13,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $660$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.r (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 392 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(392, [\chi])\).

	Total	New	Old
Modular forms	684	684	0
Cusp forms	660	660	0
Eisenstein series	24	24	0

Trace form

\( 660 q - 5 q^{2} - 5 q^{4} - 7 q^{6} - 12 q^{7} - 11 q^{8} - 328 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(392, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
392.3.r.a	$392$	$3$	392.r	392.r	$14$	$660$	$110$	$10.681$		None		$4$	$0$	\(-5\)	\(0\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{14}]$