Space of modular forms of level 3648, weight 1, and Character 3648.bf

• Label: 3648.1.bf
• Level: $3648$
• Weight: $1$
• Character orbit: 3648.bf
• Rep. character: $\chi_{3648}(353,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $640$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3648 = 2^{6} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3648.bf (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 456 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(640\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3648, [\chi])\).

	Total	New	Old
Modular forms	64	16	48
Cusp forms	16	16	0
Eisenstein series	48	0	48

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

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

Trace form

\( 16 q + 2 q^{9} + 8 q^{25} + 6 q^{33} + 8 q^{49} - 8 q^{57} + 8 q^{73} - 2 q^{81} + 4 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3648, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3648.1.bf.a	$3648$	$1$	3648.bf	456.x	$6$	$4$	$2$	$1.821$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		✓			3648.1.bf.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}^{3}q^{3}-q^{9}+(\zeta_{12}-\zeta_{12}^{5})q^{11}+\cdots\)
3648.1.bf.b	$3648$	$1$	3648.bf	456.x	$6$	$4$	$2$	$1.821$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			3648.1.bf.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{3}+(-\zeta_{12}+\zeta_{12}^{5})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
3648.1.bf.c	$3648$	$1$	3648.bf	456.x	$6$	$4$	$2$	$1.821$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		✓			3648.1.bf.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{9}+(-\zeta_{12}+\zeta_{12}^{5}+\cdots)q^{11}+\cdots\)
3648.1.bf.d	$3648$	$1$	3648.bf	456.x	$6$	$4$	$2$	$1.821$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			3648.1.bf.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}q^{3}+(-\zeta_{12}+\zeta_{12}^{5})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)