Space of modular forms of level 507, weight 2, and Character 507.s

• Label: 507.2.s
• Level: $507$
• Weight: $2$
• Character orbit: 507.s
• Rep. character: $\chi_{507}(5,\cdot)$
• Character field: $\Q(\zeta_{52})$
• Dimension: $1392$
• Newform subspaces: $1$
• Sturm bound: $121$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.s (of order \(52\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 507 \)
Character field:			\(\Q(\zeta_{52})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(121\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(507, [\chi])\).

	Total	New	Old
Modular forms	1488	1488	0
Cusp forms	1392	1392	0
Eisenstein series	96	96	0

Trace form

1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(507, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
507.2.s.a	$507$	$2$	507.s	507.s	$52$	$1392$	$58$	$4.048$		None		✓	✓	✓	507.2.s.a	$4$	$0$	\(0\)	\(-22\)	\(0\)	\(-56\)		$\mathrm{SU}(2)[C_{52}]$