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

• Label: 592.2.w
• Level: $592$
• Weight: $2$
• Character orbit: 592.w
• Rep. character: $\chi_{592}(529,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $36$
• Newform subspaces: $6$
• Sturm bound: $152$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.w (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(152\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	164	40	124
Cusp forms	140	36	104
Eisenstein series	24	4	20

Trace form

\( 36 q + 3 q^{3} + 5 q^{7} - 17 q^{9} + O(q^{10}) \)

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.w.a	$592$	$2$	592.w	37.e	$6$	$2$	$1$	$4.727$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(-3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-2\zeta_{6}q^{3}+(-2+\zeta_{6})q^{5}-2\zeta_{6}q^{7}+\cdots\)
592.2.w.b	$592$	$2$	592.w	37.e	$6$	$2$	$1$	$4.727$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{6}q^{3}+(2-\zeta_{6})q^{5}+\zeta_{6}q^{7}+(2-2\zeta_{6})q^{9}+\cdots\)
592.2.w.c	$592$	$2$	592.w	37.e	$6$	$4$	$2$	$4.727$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(-2\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(-2-2\zeta_{12}+\cdots)q^{5}+\cdots\)
592.2.w.d	$592$	$2$	592.w	37.e	$6$	$4$	$2$	$4.727$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(2\)	\(-6\)	\(8\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-2+\zeta_{12})q^{5}+\cdots\)
592.2.w.e	$592$	$2$	592.w	37.e	$6$	$4$	$2$	$4.727$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(2\)	\(6\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(2-\zeta_{12})q^{5}-2\zeta_{12}q^{7}+\cdots\)
592.2.w.f	$592$	$2$	592.w	37.e	$6$	$20$	$10$	$4.727$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(6\)	\(2\)	$2^{18}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{5}+\beta _{14})q^{3}+\beta _{4}q^{5}+(-\beta _{2}-\beta _{10}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(592, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)