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

• Label: 592.2.g
• Level: $592$
• Weight: $2$
• Character orbit: 592.g
• Rep. character: $\chi_{592}(369,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $4$
• Sturm bound: $152$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
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	82	20	62
Cusp forms	70	18	52
Eisenstein series	12	2	10

Trace form

18 * q + 4 * q^7 + 14 * q^9 - 8 * q^11 - 8 * q^21 - 18 * q^25 + 12 * q^27 - 8 * q^33 - 2 * q^37 - 8 * q^41 - 20 * q^47 - 6 * q^49 + 4 * q^53 + 48 * q^63 + 8 * q^65 + 20 * q^67 - 20 * q^71 + 16 * q^73 - 4 * q^75 - 24 * q^77 + 2 * q^81 + 12 * q^83 + 16 * q^85 + 8 * q^95 - 8 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
592.2.g.a	$592$	$2$	592.g	37.b	$2$	$2$	$2$	$4.727$	\(\Q(\sqrt{-3}) \)	None					148.2.d.a	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta q^{5}-q^{7}-2 q^{9}-3 q^{11}+\cdots\)
592.2.g.b	$592$	$2$	592.g	37.b	$2$	$2$	$2$	$4.727$	\(\Q(\sqrt{-1}) \)	None					37.2.b.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(-6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta q^{5}-3 q^{7}-2 q^{9}+3 q^{11}+\cdots\)
592.2.g.c	$592$	$2$	592.g	37.b	$2$	$4$	$4$	$4.727$	\(\Q(i, \sqrt{21})\)	None					74.2.b.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(8\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+2q^{7}+(3-\beta _{3})q^{9}+\cdots\)
592.2.g.d	$592$	$2$	592.g	37.b	$2$	$10$	$10$	$4.727$	10.0.\(\cdots\).1	None			✓		296.2.g.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{7}q^{5}+\beta _{3}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)

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

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