Space of modular forms of level 936, weight 1, and Character 936.bs

• Label: 936.1.bs
• Level: $936$
• Weight: $1$
• Character orbit: 936.bs
• Rep. character: $\chi_{936}(259,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	936.bs (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 936 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(936, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	12	12	0
Eisenstein series	8	8	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q - 6 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(936, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
936.1.bs.a	$936$	$1$	936.bs	936.as	$6$	$6$	$3$	$0.467$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-26}) \)	None		$4$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+\cdots\)
936.1.bs.b	$936$	$1$	936.bs	936.as	$6$	$6$	$3$	$0.467$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-26}) \)	None		$4$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{3}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+\cdots\)