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

• Label: 592.2.ce
• Level: $592$
• Weight: $2$
• Character orbit: 592.ce
• Rep. character: $\chi_{592}(53,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $888$
• Newform subspaces: $1$
• Sturm bound: $152$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.ce (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 592 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(152\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	936	936	0
Cusp forms	888	888	0
Eisenstein series	48	48	0

Trace form

888 * q - 12 * q^2 - 12 * q^3 - 18 * q^4 - 12 * q^5 - 24 * q^6 - 6 * q^8 - 6 * q^10 - 6 * q^11 - 12 * q^12 - 12 * q^13 - 6 * q^14 - 24 * q^15 + 18 * q^16 - 24 * q^17 + 18 * q^18 - 12 * q^19 + 72 * q^20 - 12 * q^21 - 12 * q^22 + 18 * q^24 - 6 * q^26 - 6 * q^27 - 12 * q^28 - 6 * q^29 - 54 * q^30 - 48 * q^31 - 102 * q^32 - 24 * q^33 + 18 * q^34 - 12 * q^35 - 24 * q^36 + 36 * q^37 - 108 * q^38 - 72 * q^40 + 60 * q^42 - 54 * q^44 - 6 * q^45 - 24 * q^46 - 132 * q^47 - 54 * q^48 - 24 * q^49 - 54 * q^50 + 54 * q^51 - 12 * q^52 + 12 * q^53 + 60 * q^54 - 54 * q^56 - 54 * q^58 - 12 * q^59 + 96 * q^60 - 12 * q^61 - 36 * q^62 + 108 * q^63 + 36 * q^64 - 48 * q^65 + 90 * q^66 - 12 * q^67 - 324 * q^68 - 30 * q^69 - 198 * q^70 + 108 * q^72 + 30 * q^74 - 24 * q^75 - 108 * q^76 - 30 * q^77 - 84 * q^78 - 24 * q^79 + 240 * q^80 - 24 * q^81 + 54 * q^82 + 48 * q^83 - 90 * q^84 - 6 * q^85 + 18 * q^86 + 24 * q^88 - 138 * q^90 - 12 * q^91 + 66 * q^92 - 48 * q^93 - 24 * q^95 - 84 * q^96 - 12 * q^97 - 174 * q^98 - 318 * 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.ce.a	$592$	$2$	592.ce	592.be	$36$	$888$	$74$	$4.727$		None		✓	✓	✓	592.2.ce.a	$4$	$0$	\(-12\)	\(-12\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$