Space of modular forms of level 531, weight 2, and Character 531.i

• Label: 531.2.i
• Level: $531$
• Weight: $2$
• Character orbit: 531.i
• Rep. character: $\chi_{531}(19,\cdot)$
• Character field: $\Q(\zeta_{29})$
• Dimension: $672$
• Newform subspaces: $4$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.i (of order \(29\) and degree \(28\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 59 \)
Character field:			\(\Q(\zeta_{29})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(531, [\chi])\).

	Total	New	Old
Modular forms	1792	728	1064
Cusp forms	1568	672	896
Eisenstein series	224	56	168

Trace form

672 * q + 26 * q^2 - 50 * q^4 + 25 * q^5 - 31 * q^7 + 20 * q^8 - 27 * q^10 + 27 * q^11 - 23 * q^13 + 31 * q^14 - 44 * q^16 + 26 * q^17 - 15 * q^19 + 21 * q^20 - 25 * q^22 + 13 * q^23 - 49 * q^25 + 39 * q^26 - 27 * q^28 + 41 * q^29 - 21 * q^31 + 8 * q^32 - 37 * q^34 + 36 * q^35 - 25 * q^37 + 61 * q^38 - 25 * q^40 + 21 * q^41 - 29 * q^43 + 41 * q^44 - 95 * q^46 - 16 * q^47 - 107 * q^49 - 116 * q^50 - 123 * q^52 - 29 * q^53 - 120 * q^55 - 221 * q^56 - 140 * q^58 - 23 * q^59 - 79 * q^61 - 5 * q^62 - 252 * q^64 - 66 * q^65 - 59 * q^67 - 99 * q^68 - 129 * q^70 + 10 * q^71 - 56 * q^73 - 47 * q^74 + q^76 + 43 * q^77 - 23 * q^79 + 45 * q^80 + q^82 + 35 * q^83 - 49 * q^85 + 25 * q^86 - 65 * q^88 + 9 * q^89 + 5 * q^91 + 29 * q^92 + 7 * q^94 + 43 * q^95 - 53 * q^97 - 17 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(531, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
531.2.i.a	$531$	$2$	531.i	59.c	$29$	$112$	$4$	$4.240$		None					59.2.c.a	$2$	$0$	\(26\)	\(0\)	\(25\)	\(-23\)		$\mathrm{SU}(2)[C_{29}]$
531.2.i.b	$531$	$2$	531.i	59.c	$29$	$140$	$5$	$4.240$		None					177.2.e.b	$2$	$0$	\(-1\)	\(0\)	\(-2\)	\(-2\)		$\mathrm{SU}(2)[C_{29}]$
531.2.i.c	$531$	$2$	531.i	59.c	$29$	$140$	$5$	$4.240$		None					177.2.e.a	$2$	$0$	\(1\)	\(0\)	\(2\)	\(-2\)		$\mathrm{SU}(2)[C_{29}]$
531.2.i.d	$531$	$2$	531.i	59.c	$29$	$280$	$10$	$4.240$		None		✓	✓		531.2.i.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{29}]$

Decomposition of \(S_{2}^{\mathrm{old}}(531, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(531, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)