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

• Label: 3267.1.w
• Level: $3267$
• Weight: $1$
• Character orbit: 3267.w
• Rep. character: $\chi_{3267}(118,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $396$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3267 = 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3267.w (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(396\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	360	88	272
Cusp forms	72	24	48
Eisenstein series	288	64	224

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	16	0

Trace form

\( 24 q - q^{4} + 3 q^{5} + O(q^{10}) \)

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.w.a	$3267$	$1$	3267.w	99.o	$30$	$8$	$1$	$1.630$	\(\Q(\zeta_{15})\)	$D_{3}$	\(\Q(\sqrt{-11}) \)	None		$16$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q-\zeta_{30}^{13}q^{4}-\zeta_{30}q^{5}-\zeta_{30}^{11}q^{16}+\cdots\)
3267.1.w.b	$3267$	$1$	3267.w	99.o	$30$	$16$	$2$	$1.630$	16.0.\(\cdots\).1	$S_{4}$	None	None		$16$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{2}-\beta _{8}-\beta _{10}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3267, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3267, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(1089, [\chi])\)\(^{\oplus 2}\)