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

• Label: 507.2.t
• Level: $507$
• Weight: $2$
• Character orbit: 507.t
• Rep. character: $\chi_{507}(4,\cdot)$
• Character field: $\Q(\zeta_{78})$
• Dimension: $696$
• 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.t (of order \(78\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{78})\)
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	1512	696	816
Cusp forms	1416	696	720
Eisenstein series	96	0	96

Trace form

\( 696 q - q^{3} - 26 q^{4} + 3 q^{7} + 29 q^{9} + O(q^{10}) \)

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.t.a	$507$	$2$	507.t	169.k	$78$	$336$	$14$	$4.048$		None		$2$	$0$	\(0\)	\(14\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{78}]$
507.2.t.b	$507$	$2$	507.t	169.k	$78$	$360$	$15$	$4.048$		None		$2$	$0$	\(0\)	\(-15\)	\(0\)	\(3\)		$\mathrm{SU}(2)[C_{78}]$

Decomposition of \(S_{2}^{\mathrm{old}}(507, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(507, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)