Space of modular forms of level 592, weight 1, and Character 592.bt

• Label: 592.1.bt
• Level: $592$
• Weight: $1$
• Character orbit: 592.bt
• Rep. character: $\chi_{592}(95,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $76$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	592.bt (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 148 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(76\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(592, [\chi])\).

	Total	New	Old
Modular forms	42	6	36
Cusp forms	6	6	0
Eisenstein series	36	0	36

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(592, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
592.1.bt.a	$592$	$1$	592.bt	148.o	$18$	$6$	$1$	$0.295$	\(\Q(\zeta_{18})\)	$D_{18}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$		\(q+(-\zeta_{18}^{2}-\zeta_{18}^{3})q^{5}+\zeta_{18}^{8}q^{9}+\cdots\)