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

• Label: 507.2.x
• Level: $507$
• Weight: $2$
• Character orbit: 507.x
• Rep. character: $\chi_{507}(2,\cdot)$
• Character field: $\Q(\zeta_{156})$
• Dimension: $2832$
• Newform subspaces: $2$
• Sturm bound: $121$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.x (of order \(156\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 507 \)
Character field:			\(\Q(\zeta_{156})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(121\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	3024	3024	0
Cusp forms	2832	2832	0
Eisenstein series	192	192	0

Trace form

2832 * q - 50 * q^3 - 92 * q^4 - 50 * q^6 - 90 * q^7 - 50 * q^9 - 116 * q^10 - 52 * q^12 - 112 * q^13 - 38 * q^15 - 212 * q^16 - 56 * q^18 - 102 * q^19 - 74 * q^21 - 48 * q^22 + 86 * q^24 - 104 * q^25 - 32 * q^27 - 104 * q^28 - 174 * q^30 - 98 * q^31 - 68 * q^33 - 68 * q^34 - 16 * q^36 - 74 * q^37 - 118 * q^39 - 96 * q^40 - 44 * q^42 - 134 * q^43 + 98 * q^45 - 58 * q^48 - 122 * q^49 - 52 * q^51 - 180 * q^52 - 98 * q^54 - 324 * q^55 - 80 * q^57 - 132 * q^58 - 96 * q^60 - 124 * q^61 - 198 * q^63 - 104 * q^64 + 58 * q^66 + 112 * q^67 + 26 * q^69 + 136 * q^70 - 64 * q^72 - 42 * q^73 - 164 * q^75 - 68 * q^76 + 28 * q^78 - 120 * q^79 - 38 * q^81 - 340 * q^82 - 44 * q^84 - 116 * q^85 - 34 * q^87 + 116 * q^88 - 52 * q^90 - 114 * q^91 + 68 * q^93 + 36 * q^94 - 406 * q^96 - 86 * q^97 - 92 * 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.x.a	$507$	$2$	507.x	507.x	$156$	$48$	$1$	$4.048$		\(\Q(\sqrt{-3}) \)		✓			507.2.x.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$\mathrm{U}(1)[D_{156}]$
507.2.x.b	$507$	$2$	507.x	507.x	$156$	$2784$	$58$	$4.048$		None		✓	✓		507.2.x.b	$4$	$0$	\(0\)	\(-50\)	\(0\)	\(-100\)		$\mathrm{SU}(2)[C_{156}]$