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

• Label: 1083.1.b
• Level: $1083$
• Weight: $1$
• Character orbit: 1083.b
• Rep. character: $\chi_{1083}(362,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $126$
• Trace bound: $3$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	22	19	3
Cusp forms	2	2	0
Eisenstein series	20	17	3

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

\( 2 q + 2 q^{4} - 2 q^{7} + 2 q^{9} + O(q^{10}) \)

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.b.a	$1083$	$1$	1083.b	3.b	$2$	$1$	$1$	$0.540$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None	✓				57.1.h.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-q^{3}+q^{4}-q^{7}+q^{9}-q^{12}+q^{13}+\cdots\)
1083.1.b.b	$1083$	$1$	1083.b	3.b	$2$	$1$	$1$	$0.540$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None	✓				57.1.h.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+q^{3}+q^{4}-q^{7}+q^{9}+q^{12}-q^{13}+\cdots\)