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

• Label: 592.2.bx
• Level: $592$
• Weight: $2$
• Character orbit: 592.bx
• Rep. character: $\chi_{592}(15,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $228$
• Newform subspaces: $6$
• Sturm bound: $152$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bx (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 148 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(152\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	984	228	756
Cusp forms	840	228	612
Eisenstein series	144	0	144

Trace form

\( 228 q + 18 q^{5} + O(q^{10}) \)

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.bx.a	$592$	$2$	592.bx	148.q	$36$	$12$	$1$	$4.727$	\(\Q(\zeta_{36})\)	None		$2$	$0$	\(0\)	\(-6\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{36}]$	\(q+(-\zeta_{36}^{2}+\zeta_{36}^{4}-\zeta_{36}^{6})q^{3}+(-\zeta_{36}^{3}+\cdots)q^{5}+\cdots\)
592.2.bx.b	$592$	$2$	592.bx	148.q	$36$	$12$	$1$	$4.727$	\(\Q(\zeta_{36})\)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{36}]$	\(q+(-1+2\zeta_{36}^{2}-2\zeta_{36}^{3}+\zeta_{36}^{6}+\cdots)q^{5}+\cdots\)
592.2.bx.c	$592$	$2$	592.bx	148.q	$36$	$12$	$1$	$4.727$	\(\Q(\zeta_{36})\)	None		$2$	$0$	\(0\)	\(6\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{36}]$	\(q+(\zeta_{36}^{2}-\zeta_{36}^{4}+\zeta_{36}^{6})q^{3}+(-\zeta_{36}^{3}+\cdots)q^{5}+\cdots\)
592.2.bx.d	$592$	$2$	592.bx	148.q	$36$	$60$	$5$	$4.727$		None		$2$	$0$	\(0\)	\(-6\)	\(12\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$
592.2.bx.e	$592$	$2$	592.bx	148.q	$36$	$60$	$5$	$4.727$		None		$2$	$0$	\(0\)	\(6\)	\(12\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$
592.2.bx.f	$592$	$2$	592.bx	148.q	$36$	$72$	$6$	$4.727$		None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$

Decomposition of \(S_{2}^{\mathrm{old}}(592, [\chi])\) into lower level spaces

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