Space of modular forms of level 1044, weight 1, and Character 1044.ba

• Label: 1044.1.ba
• Level: $1044$
• Weight: $1$
• Character orbit: 1044.ba
• Rep. character: $\chi_{1044}(91,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1044 = 2^{2} \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1044.ba (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 116 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1044, [\chi])\).

	Total	New	Old
Modular forms	60	24	36
Cusp forms	12	12	0
Eisenstein series	48	12	36

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + 2 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1044, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1044.1.ba.a	$1044$	$1$	1044.ba	116.h	$14$	$12$	$2$	$0.521$	\(\Q(\zeta_{28})\)	$D_{14}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	1044.1.ba.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{28}^{3}q^{2}+\zeta_{28}^{6}q^{4}+(-\zeta_{28}+\zeta_{28}^{5}+\cdots)q^{5}+\cdots\)