Space of modular forms of level 155, weight 1, and Character 155.c

• Label: 155.1.c
• Level: $155$
• Weight: $1$
• Character orbit: 155.c
• Rep. character: $\chi_{155}(154,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	155.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(155, [\chi])\).

	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

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

Decomposition of \(S_{1}^{\mathrm{new}}(155, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
155.1.c.a	$155$	$1$	155.c	155.c	$2$	$1$	$1$	$0.077$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-155}) \)	\(\Q(\sqrt{5}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+q^{4}-q^{5}-q^{9}+q^{16}-2q^{19}-q^{20}+\cdots\)
155.1.c.b	$155$	$1$	155.c	155.c	$2$	$2$	$2$	$0.077$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-31}) \)	None		$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots\)