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

• Label: 592.2.by
• Level: $592$
• Weight: $2$
• Character orbit: 592.by
• Rep. character: $\chi_{592}(21,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $888$
• 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.by (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 592 \)
Character field:			\(\Q(\zeta_{36})\)
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	936	936	0
Cusp forms	888	888	0
Eisenstein series	48	48	0

Trace form

\( 888 q - 12 q^{2} - 12 q^{3} - 18 q^{4} - 12 q^{5} - 18 q^{8} + O(q^{10}) \)

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.by.a	$592$	$2$	592.by	592.ay	$36$	$888$	$74$	$4.727$		None		$4$	$0$	\(-12\)	\(-12\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$