Space of modular forms of level 786, weight 2, and Character 786.o

• Label: 786.2.o
• Level: $786$
• Weight: $2$
• Character orbit: 786.o
• Rep. character: $\chi_{786}(17,\cdot)$
• Character field: $\Q(\zeta_{130})$
• Dimension: $2112$
• Newform subspaces: $2$
• Sturm bound: $264$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 786 = 2 \cdot 3 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	786.o (of order \(130\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 393 \)
Character field:			\(\Q(\zeta_{130})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(264\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(786, [\chi])\).

	Total	New	Old
Modular forms	6528	2112	4416
Cusp forms	6144	2112	4032
Eisenstein series	384	0	384

Trace form

\( 2112 q + 2 q^{3} + 44 q^{4} - 4 q^{7} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(786, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
786.2.o.a	$786$	$2$	786.o	393.p	$130$	$1056$	$22$	$6.276$		None		$2$	$0$	\(-22\)	\(1\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{130}]$
786.2.o.b	$786$	$2$	786.o	393.p	$130$	$1056$	$22$	$6.276$		None		$2$	$0$	\(22\)	\(1\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{130}]$

Decomposition of \(S_{2}^{\mathrm{old}}(786, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(786, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(393, [\chi])\)\(^{\oplus 2}\)