Space of modular forms of level 392, weight 2, and Character 392.z

• Label: 392.2.z
• Level: $392$
• Weight: $2$
• Character orbit: 392.z
• Rep. character: $\chi_{392}(37,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $648$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 392 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(392, [\chi])\).

	Total	New	Old
Modular forms	696	696	0
Cusp forms	648	648	0
Eisenstein series	48	48	0

Trace form

\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(392, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
392.2.z.a	$392$	$2$	392.z	392.z	$42$	$648$	$54$	$3.130$		None		$4$	$0$	\(-13\)	\(0\)	\(0\)	\(-24\)		$\mathrm{SU}(2)[C_{42}]$