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

• Label: 3267.1.h
• Level: $3267$
• Weight: $1$
• Character orbit: 3267.h
• Rep. character: $\chi_{3267}(604,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• 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.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{6})\)
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	96	20	76
Cusp forms	24	4	20
Eisenstein series	72	16	56

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	4	0

Trace form

\( 4 q + 2 q^{4} - 2 q^{5} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3267.1.h.a	$3267$	$1$	3267.h	99.h	$6$	$4$	$2$	$1.630$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None			✓	✓	1089.1.h.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{2}q^{5}+\beta _{1}q^{7}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3267, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1089, [\chi])\)\(^{\oplus 2}\)