Space of modular forms of level 592, weight 2, and Character 592.bj

• Label: 592.2.bj
• Level: $592$
• Weight: $2$
• Character orbit: 592.bj
• Rep. character: $\chi_{592}(269,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $296$
• Newform subspaces: $1$
• Sturm bound: $152$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bj (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 592 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(152\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(592, [\chi])\).

	Total	New	Old
Modular forms	312	312	0
Cusp forms	296	296	0
Eisenstein series	16	16	0

Trace form

\( 296 q - 2 q^{2} - 2 q^{3} - 2 q^{5} - 8 q^{6} - 8 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(592, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
592.2.bj.a	$592$	$2$	592.bj	592.aj	$12$	$296$	$74$	$4.727$		None		$4$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$