Space of modular forms of level 387, weight 4, and Character 387.t

• Label: 387.4.t
• Level: $387$
• Weight: $4$
• Character orbit: 387.t
• Rep. character: $\chi_{387}(80,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $1$
• Sturm bound: $176$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	387.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 129 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(176\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(387, [\chi])\).

	Total	New	Old
Modular forms	272	88	184
Cusp forms	256	88	168
Eisenstein series	16	0	16

Trace form

\( 88 q + 352 q^{4} + 36 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(387, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
387.4.t.a	$387$	$4$	387.t	129.h	$6$	$88$	$44$	$22.834$		None		✓	387.4.t.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(36\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(387, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(387, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(129, [\chi])\)\(^{\oplus 2}\)