Space of modular forms of level 180, weight 1, and Character 180.f

• Label: 180.1.f
• Level: $180$
• Weight: $1$
• Character orbit: 180.f
• Rep. character: $\chi_{180}(19,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	180.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(180, [\chi])\).

	Total	New	Old
Modular forms	10	4	6
Cusp forms	2	2	0
Eisenstein series	8	2	6

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(180, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
180.1.f.a	$180$	$1$	180.f	20.d	$2$	$2$	$2$	$0.090$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \)	\(\Q(\sqrt{15}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{2}-q^{4}-iq^{5}+iq^{8}-q^{10}+\cdots\)