Space of modular forms of level 1083, weight 1, and Character 1083.l

• Label: 1083.1.l
• Level: $1083$
• Weight: $1$
• Character orbit: 1083.l
• Rep. character: $\chi_{1083}(62,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $126$
• Trace bound: $12$

Defining parameters

Level:	\( N \)	\(=\)	\( 1083 = 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1083.l (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(126\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1083, [\chi])\).

	Total	New	Old
Modular forms	132	108	24
Cusp forms	12	12	0
Eisenstein series	120	96	24

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

\( 12 q + 6 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1083, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1083.1.l.a	$1083$	$1$	1083.l	57.l	$18$	$6$	$1$	$0.540$	\(\Q(\zeta_{18})\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None					57.1.h.a	$12$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$		\(q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{7}+\cdots\)
1083.1.l.b	$1083$	$1$	1083.l	57.l	$18$	$6$	$1$	$0.540$	\(\Q(\zeta_{18})\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None					57.1.h.a	$12$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$		\(q-\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{7}+\cdots\)