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

\( 2832 q - 50 q^{3} - 92 q^{4} - 50 q^{6} - 90 q^{7} - 50 q^{9} + O(q^{10}) \)

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	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	$156$	$48$	$1$	$4.048$		\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$\mathrm{U}(1)[D_{156}]$
507.2.x.b	$507$	$2$	507.x	507.x	$156$	$2784$	$58$	$4.048$		None		$4$	$0$	\(0\)	\(-50\)	\(0\)	\(-100\)		$\mathrm{SU}(2)[C_{156}]$