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

• Label: 3267.1.m
• Level: $3267$
• Weight: $1$
• Character orbit: 3267.m
• Rep. character: $\chi_{3267}(269,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $32$
• Newform subspaces: $5$
• Sturm bound: $396$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 3267 = 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3267.m (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(396\)
Trace bound:			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	188	32	156
Cusp forms	44	32	12
Eisenstein series	144	0	144

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

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

Trace form

\( 32 q - 4 q^{31} - 32 q^{34} - 4 q^{49} - 8 q^{64} - 16 q^{67} + 8 q^{70} + 8 q^{82} + 8 q^{97}+O(q^{100}) \)

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.m.a	$3267$	$1$	3267.m	33.h	$10$	$4$	$1$	$1.630$	\(\Q(\zeta_{10})\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓			3267.1.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+\zeta_{10}^{2}q^{4}+\zeta_{10}^{2}q^{7}-\zeta_{10}q^{13}+\cdots\)
3267.1.m.b	$3267$	$1$	3267.m	33.h	$10$	$4$	$1$	$1.630$	\(\Q(\zeta_{10})\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓			3267.1.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q+\zeta_{10}^{2}q^{4}-\zeta_{10}^{2}q^{7}+\zeta_{10}q^{13}+\cdots\)
3267.1.m.c	$3267$	$1$	3267.m	33.h	$10$	$8$	$2$	$1.630$	8.0.324000000.3	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			3267.1.b.e	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-1-\beta _{2}-\beta _{4}-\beta _{6})q^{4}+\beta _{3}q^{7}+\cdots\)
3267.1.m.d	$3267$	$1$	3267.m	33.h	$10$	$8$	$2$	$1.630$	8.0.64000000.1	$S_{4}$	None	None		✓			3267.1.b.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-\beta _{7}q^{2}-\beta _{4}q^{4}-\beta _{3}q^{5}+\beta _{4}q^{7}+\cdots\)
3267.1.m.e	$3267$	$1$	3267.m	33.h	$10$	$8$	$2$	$1.630$	8.0.64000000.1	$S_{4}$	None	None		✓			3267.1.b.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+\beta _{7}q^{2}-\beta _{4}q^{4}-\beta _{3}q^{5}-\beta _{4}q^{7}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3267, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 3}\)