Space of modular forms of level 2183, weight 1, and Character 2183.d

• Label: 2183.1.d
• Level: $2183$
• Weight: $1$
• Character orbit: 2183.d
• Rep. character: $\chi_{2183}(2182,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $8$
• Sturm bound: $190$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2183 = 37 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2183.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2183 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(190\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2183, [\chi])\).

	Total	New	Old
Modular forms	26	26	0
Cusp forms	24	24	0
Eisenstein series	2	2	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	4	0

Trace form

\( 24 q - 2 q^{3} + 18 q^{4} - 6 q^{7} + 14 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2183, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2183.1.d.a	$2183$	$1$	2183.d	2183.d	$2$	$1$	$1$	$1.089$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2183}) \)	None	✓	$2$	$0$	\(-1\)	\(2\)	\(0\)	\(-1\)	$1$		\(q-q^{2}+2q^{3}-2q^{6}-q^{7}+q^{8}+3q^{9}+\cdots\)
2183.1.d.b	$2183$	$1$	2183.d	2183.d	$2$	$1$	$1$	$1.089$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2183}) \)	None	✓	$2$	$0$	\(1\)	\(2\)	\(0\)	\(-1\)	$1$		\(q+q^{2}+2q^{3}+2q^{6}-q^{7}-q^{8}+3q^{9}+\cdots\)
2183.1.d.c	$2183$	$1$	2183.d	2183.d	$2$	$2$	$2$	$1.089$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-q^{2}-\beta q^{5}-q^{7}+q^{8}-q^{9}+\beta q^{10}+\cdots\)
2183.1.d.d	$2183$	$1$	2183.d	2183.d	$2$	$2$	$2$	$1.089$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+q^{2}-\beta q^{5}-q^{7}-q^{8}-q^{9}-\beta q^{10}+\cdots\)
2183.1.d.e	$2183$	$1$	2183.d	2183.d	$2$	$3$	$3$	$1.089$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-2183}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2183.1.d.f	$2183$	$1$	2183.d	2183.d	$2$	$3$	$3$	$1.089$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-2183}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2183.1.d.g	$2183$	$1$	2183.d	2183.d	$2$	$6$	$6$	$1.089$	\(\Q(\zeta_{21})^+\)	$D_{21}$	\(\Q(\sqrt{-2183}) \)	None	✓	$2$	$0$	\(-1\)	\(-2\)	\(0\)	\(1\)	$1$		\(q+(-1+\beta _{1}-\beta _{3}+\beta _{5})q^{2}+\beta _{3}q^{3}+\cdots\)
2183.1.d.h	$2183$	$1$	2183.d	2183.d	$2$	$6$	$6$	$1.089$	\(\Q(\zeta_{21})^+\)	$D_{21}$	\(\Q(\sqrt{-2183}) \)	None	✓	$2$	$0$	\(1\)	\(-2\)	\(0\)	\(1\)	$1$		\(q+\beta _{4}q^{2}-\beta _{5}q^{3}+(2-\beta _{1}+\beta _{3}-\beta _{5})q^{4}+\cdots\)