Space of modular forms of level 3267, weight 1, and Character 3267.bf

• Label: 3267.1.bf
• Level: $3267$
• Weight: $1$
• Character orbit: 3267.bf
• Rep. character: $\chi_{3267}(40,\cdot)$
• Character field: $\Q(\zeta_{90})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $396$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3267 = 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3267.bf (of order \(90\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 297 \)
Character field:			\(\Q(\zeta_{90})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(396\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3267, [\chi])\).

	Total	New	Old
Modular forms	312	216	96
Cusp forms	24	24	0
Eisenstein series	288	192	96

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + 3 q^{5} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3267, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3267.1.bf.a	$3267$	$1$	3267.bf	297.w	$90$	$24$	$1$	$1.630$	\(\Q(\zeta_{45})\)	$D_{9}$	\(\Q(\sqrt{-11}) \)	None		$16$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$		\(q+\zeta_{90}^{34}q^{3}-\zeta_{90}^{31}q^{4}+(\zeta_{90}^{32}+\cdots)q^{5}+\cdots\)