Space of modular forms of level 532, weight 2, and Character 532.cj

• Label: 532.2.cj
• Level: $532$
• Weight: $2$
• Character orbit: 532.cj
• Rep. character: $\chi_{532}(33,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $78$
• Newform subspaces: $1$
• Sturm bound: $160$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.cj (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(160\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(532, [\chi])\).

	Total	New	Old
Modular forms	516	78	438
Cusp forms	444	78	366
Eisenstein series	72	0	72

Trace form

78 * q + 6 * q^7 - 6 * q^11 + 6 * q^13 - 3 * q^15 + 27 * q^17 + 21 * q^19 - 3 * q^21 - 24 * q^23 + 12 * q^27 - 18 * q^29 + 33 * q^35 + 36 * q^37 - 18 * q^39 - 18 * q^41 - 48 * q^43 - 18 * q^45 - 18 * q^49 + 6 * q^53 - 18 * q^57 + 45 * q^59 + 39 * q^61 - 27 * q^63 - 18 * q^65 + 21 * q^67 + 6 * q^71 - 3 * q^73 - 21 * q^75 - 21 * q^77 + 36 * q^79 + 36 * q^81 - 18 * q^83 + 60 * q^85 - 21 * q^91 - 102 * q^93 + 60 * q^95 - 27 * q^97 + 27 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(532, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
532.2.cj.a	$532$	$2$	532.cj	133.af	$18$	$78$	$13$	$4.248$		None		✓	✓	✓	532.2.bw.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(532, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(532, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 2}\)