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

• Label: 1053.1.k
• Level: $1053$
• Weight: $1$
• Character orbit: 1053.k
• Rep. character: $\chi_{1053}(107,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• 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.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
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	26	6	20
Cusp forms	2	2	0
Eisenstein series	24	4	20

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + 2 q^{4} - 2 q^{7} - q^{13} + 2 q^{16} + q^{19} - q^{25} - 2 q^{28} + q^{31} + q^{37} + q^{43} - 3 q^{49} - q^{52} + q^{61} + 2 q^{64} + q^{67} - 2 q^{73} + q^{76} + q^{79} - 2 q^{91} + q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1053.1.k.a	$1053$	$1$	1053.k	117.k	$6$	$2$	$1$	$0.526$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None			✓	✓	351.1.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+q^{4}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{13}+q^{16}+\cdots\)