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

• Label: 592.1.k
• Level: $592$
• Weight: $1$
• Character orbit: 592.k
• Rep. character: $\chi_{592}(401,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $76$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	592.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(76\)
Trace bound:			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	26	6	20
Cusp forms	14	4	10
Eisenstein series	12	2	10

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	4	0

Trace form

\( 4 q - 2 q^{5} + 4 q^{7} + O(q^{10}) \)

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.k.a	$592$	$1$	592.k	37.d	$4$	$2$	$1$	$0.295$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$1$		\(q+iq^{3}+(-1-i)q^{5}+q^{7}+iq^{11}+\cdots\)
592.1.k.b	$592$	$1$	592.k	37.d	$4$	$2$	$1$	$0.295$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-iq^{3}+q^{7}+iq^{11}+(-1-i)q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(592, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(592, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)