Space of modular forms of level 387, weight 2, and Character 387.bc

• Label: 387.2.bc
• Level: $387$
• Weight: $2$
• Character orbit: 387.bc
• Rep. character: $\chi_{387}(26,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $168$
• Newform subspaces: $1$
• Sturm bound: $88$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.bc (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 129 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(88\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(387, [\chi])\).

	Total	New	Old
Modular forms	576	168	408
Cusp forms	480	168	312
Eisenstein series	96	0	96

Trace form

\( 168 q - 24 q^{4} - 6 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(387, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
387.2.bc.a	$387$	$2$	387.bc	129.n	$42$	$168$	$14$	$3.090$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{42}]$

Decomposition of \(S_{2}^{\mathrm{old}}(387, [\chi])\) into lower level spaces

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