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

• Label: 3648.1.bl
• Level: $3648$
• Weight: $1$
• Character orbit: 3648.bl
• Rep. character: $\chi_{3648}(1793,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $640$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 3648 = 2^{6} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3648.bl (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(640\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	72	12	60
Cusp forms	24	4	20
Eisenstein series	48	8	40

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

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

Trace form

\( 4 q - 2 q^{9} - 2 q^{13} - 2 q^{21} - 2 q^{25} + 4 q^{37} - 2 q^{57} - 2 q^{61} + 2 q^{73} - 2 q^{81} - 2 q^{93} - 4 q^{97}+O(q^{100}) \)

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.bl.a	$3648$	$1$	3648.bl	57.h	$6$	$2$	$1$	$1.821$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None					57.1.h.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)	$1$		\(q+\zeta_{6}^{2}q^{3}+q^{7}-\zeta_{6}q^{9}-\zeta_{6}q^{13}+\cdots\)
3648.1.bl.b	$3648$	$1$	3648.bl	57.h	$6$	$2$	$1$	$1.821$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None					57.1.h.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{6}^{2}q^{3}-q^{7}-\zeta_{6}q^{9}-\zeta_{6}q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3648, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3648, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 3}\)