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

• Label: 786.2.i
• Level: $786$
• Weight: $2$
• Character orbit: 786.i
• Rep. character: $\chi_{786}(193,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $264$
• Newform subspaces: $4$
• Sturm bound: $264$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 786 = 2 \cdot 3 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	786.i (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 131 \)
Character field:			\(\Q(\zeta_{13})\)
Newform subspaces:			\( 4 \)
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	1632	264	1368
Cusp forms	1536	264	1272
Eisenstein series	96	0	96

Trace form

\( 264 q - 22 q^{4} + 8 q^{5} + 2 q^{6} + 12 q^{7} - 22 q^{9} + O(q^{10}) \)

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.i.a	$786$	$2$	786.i	131.e	$13$	$60$	$5$	$6.276$		None		$2$	$0$	\(-5\)	\(-5\)	\(8\)	\(7\)		$\mathrm{SU}(2)[C_{13}]$
786.2.i.b	$786$	$2$	786.i	131.e	$13$	$60$	$5$	$6.276$		None		$2$	$0$	\(5\)	\(5\)	\(-2\)	\(3\)		$\mathrm{SU}(2)[C_{13}]$
786.2.i.c	$786$	$2$	786.i	131.e	$13$	$72$	$6$	$6.276$		None		$2$	$0$	\(-6\)	\(6\)	\(0\)	\(3\)		$\mathrm{SU}(2)[C_{13}]$
786.2.i.d	$786$	$2$	786.i	131.e	$13$	$72$	$6$	$6.276$		None		$2$	$0$	\(6\)	\(-6\)	\(2\)	\(-1\)		$\mathrm{SU}(2)[C_{13}]$

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

\( S_{2}^{\mathrm{old}}(786, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(131, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(262, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(393, [\chi])\)\(^{\oplus 2}\)