Space of modular forms of level 1386, weight 4, and Character 1386.g

• Label: 1386.4.g
• Level: $1386$
• Weight: $4$
• Character orbit: 1386.g
• Rep. character: $\chi_{1386}(881,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $1152$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1386.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1152\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1386, [\chi])\).

	Total	New	Old
Modular forms	880	80	800
Cusp forms	848	80	768
Eisenstein series	32	0	32

Trace form

\( 80 q - 320 q^{4} - 56 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1386, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1386.4.g.a	$1386$	$4$	1386.g	21.c	$2$	$40$	$40$	$81.777$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-88\)		$\mathrm{SU}(2)[C_{2}]$
1386.4.g.b	$1386$	$4$	1386.g	21.c	$2$	$40$	$40$	$81.777$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(32\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)