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

• Label: 592.2.i
• Level: $592$
• Weight: $2$
• Character orbit: 592.i
• Rep. character: $\chi_{592}(417,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $36$
• Newform subspaces: $8$
• Sturm bound: $152$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
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	164	40	124
Cusp forms	140	36	104
Eisenstein series	24	4	20

Trace form

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

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.i.a	$592$	$2$	592.i	37.c	$3$	$2$	$1$	$4.727$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(-3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{3}-3\zeta_{6}q^{5}-4\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots\)
592.2.i.b	$592$	$2$	592.i	37.c	$3$	$2$	$1$	$4.727$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{3}-3\zeta_{6}q^{5}+3\zeta_{6}q^{7}+(2-2\zeta_{6})q^{9}+\cdots\)
592.2.i.c	$592$	$2$	592.i	37.c	$3$	$2$	$1$	$4.727$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+2\zeta_{6}q^{7}+(3-3\zeta_{6})q^{9}+2q^{11}+\cdots\)
592.2.i.d	$592$	$2$	592.i	37.c	$3$	$2$	$1$	$4.727$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{3}+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{9}+\cdots\)
592.2.i.e	$592$	$2$	592.i	37.c	$3$	$6$	$3$	$4.727$	6.0.4406832.1	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{3}+(-\beta _{1}-\beta _{5})q^{5}-\beta _{4}q^{7}+\cdots\)
592.2.i.f	$592$	$2$	592.i	37.c	$3$	$6$	$3$	$4.727$	6.0.27870912.1	None		$2$	$0$	\(0\)	\(1\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{4})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
592.2.i.g	$592$	$2$	592.i	37.c	$3$	$6$	$3$	$4.727$	6.0.591408.1	None		$2$	$0$	\(0\)	\(2\)	\(1\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(\beta _{1}+\beta _{5})q^{5}+\cdots\)
592.2.i.h	$592$	$2$	592.i	37.c	$3$	$10$	$5$	$4.727$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(1\)	\(3\)	\(-3\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{9}q^{3}+(\beta _{2}+\beta _{6}+\beta _{9})q^{5}+(-1+\cdots)q^{7}+\cdots\)

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

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