Space of modular forms of level 183, weight 1, and Character 183.d

• Label: 183.1.d
• Level: $183$
• Weight: $1$
• Character orbit: 183.d
• Rep. character: $\chi_{183}(182,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $20$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 183 = 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	183.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 183 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(20\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(183, [\chi])\).

	Total	New	Old
Modular forms	5	5	0
Cusp forms	3	3	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	3	0	0	0

Trace form

\( 3 q - q^{3} + q^{4} + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(183, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
183.1.d.a	$183$	$1$	183.d	183.d	$2$	$1$	$1$	$0.091$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-183}) \)	\(\Q(\sqrt{61}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{3}-q^{4}+q^{9}-q^{12}-2q^{13}+q^{16}+\cdots\)
183.1.d.b	$183$	$1$	183.d	183.d	$2$	$2$	$2$	$0.091$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-183}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{9}+\beta q^{11}+\cdots\)