Space of modular forms of level 1053, weight 1, and Character 1053.bb

• Label: 1053.1.bb
• Level: $1053$
• Weight: $1$
• Character orbit: 1053.bb
• Rep. character: $\chi_{1053}(109,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $126$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1053 = 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1053.bb (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(126\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1053, [\chi])\).

	Total	New	Old
Modular forms	52	12	40
Cusp forms	4	4	0
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

\( 4 q + 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1053, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1053.1.bb.a	$1053$	$1$	1053.bb	117.y	$12$	$4$	$1$	$0.526$	\(\Q(\zeta_{12})\)	$D_{4}$	\(\Q(\sqrt{-3}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+\zeta_{12}^{5}q^{4}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}-\zeta_{12}^{5}q^{13}+\cdots\)