Space of modular forms of level 171, weight 1, and Character 171.c

• Label: 171.1.c
• Level: $171$
• Weight: $1$
• Character orbit: 171.c
• Rep. character: $\chi_{171}(37,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	171.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(171, [\chi])\).

	Total	New	Old
Modular forms	5	2	3
Cusp forms	1	1	0
Eisenstein series	4	1	3

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(171, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
171.1.c.a	$171$	$1$	171.c	19.b	$2$	$1$	$1$	$0.085$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{57}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+q^{4}-2q^{7}+q^{16}-q^{19}-q^{25}+\cdots\)