Space of modular forms of level 387, weight 3, and Character 387.bi

• Label: 387.3.bi
• Level: $387$
• Weight: $3$
• Character orbit: 387.bi
• Rep. character: $\chi_{387}(14,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $1032$
• Newform subspaces: $1$
• Sturm bound: $132$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	387.bi (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 387 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(132\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(387, [\chi])\).

	Total	New	Old
Modular forms	1080	1080	0
Cusp forms	1032	1032	0
Eisenstein series	48	48	0

Trace form

\( 1032 q - 15 q^{2} - 9 q^{3} - 173 q^{4} - 21 q^{5} + 14 q^{6} - 16 q^{7} + 39 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(387, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
387.3.bi.a	$387$	$3$	387.bi	387.ai	$42$	$1032$	$86$	$10.545$		None		$2$	$0$	\(-15\)	\(-9\)	\(-21\)	\(-16\)		$\mathrm{SU}(2)[C_{42}]$