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

• Label: 531.2.p
• Level: $531$
• Weight: $2$
• Character orbit: 531.p
• Rep. character: $\chi_{531}(2,\cdot)$
• Character field: $\Q(\zeta_{174})$
• Dimension: $3248$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.p (of order \(174\) and degree \(56\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 531 \)
Character field:			\(\Q(\zeta_{174})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	3472	3472	0
Cusp forms	3248	3248	0
Eisenstein series	224	224	0

Trace form

3248 * q - 87 * q^2 - 54 * q^3 + 29 * q^4 - 87 * q^5 - 58 * q^6 - 27 * q^7 - 62 * q^9 - 116 * q^10 - 87 * q^11 - 66 * q^12 - 29 * q^13 - 87 * q^14 - 73 * q^15 + 29 * q^16 - 58 * q^18 - 96 * q^19 - 69 * q^20 - 48 * q^21 - 41 * q^22 - 87 * q^23 - 58 * q^24 - 71 * q^25 - 45 * q^27 - 132 * q^28 - 81 * q^29 - 58 * q^30 - 29 * q^31 - 87 * q^32 - 58 * q^33 - 29 * q^34 - 70 * q^36 - 116 * q^37 - 87 * q^38 - 58 * q^39 - 29 * q^40 - 15 * q^41 - 58 * q^42 - 29 * q^43 - 50 * q^45 - 116 * q^46 - 87 * q^47 - 270 * q^48 + 19 * q^49 - 87 * q^50 + 142 * q^51 - 29 * q^52 - 261 * q^54 - 116 * q^55 - 87 * q^56 - 155 * q^57 - 135 * q^59 + 632 * q^60 - 29 * q^61 - 259 * q^63 - 256 * q^64 - 87 * q^65 - 307 * q^66 - 29 * q^67 + 3 * q^68 + 174 * q^69 - 29 * q^70 - 232 * q^72 - 116 * q^73 - 177 * q^74 + 7 * q^75 - 45 * q^76 - 87 * q^77 + 16 * q^78 - 39 * q^79 - 70 * q^81 - 116 * q^82 - 87 * q^83 + 6 * q^84 - 37 * q^85 - 63 * q^86 - 111 * q^87 - 65 * q^88 - 58 * q^90 - 116 * q^91 - 87 * q^92 - 58 * q^93 - 29 * q^94 + 9 * q^95 - 58 * q^96 - 29 * q^97 - 58 * q^99

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.p.a	$531$	$2$	531.p	531.p	$174$	$3248$	$58$	$4.240$		None		✓	✓	✓	531.2.p.a	$4$	$0$	\(-87\)	\(-54\)	\(-87\)	\(-27\)		$\mathrm{SU}(2)[C_{174}]$