Space of modular forms of level 155, weight 2, and Character 155.r

• Label: 155.2.r
• Level: $155$
• Weight: $2$
• Character orbit: 155.r
• Rep. character: $\chi_{155}(23,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $112$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.r (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(155, [\chi])\).

	Total	New	Old
Modular forms	144	144	0
Cusp forms	112	112	0
Eisenstein series	32	32	0

Trace form

\( 112 q - 6 q^{2} - 10 q^{3} - 16 q^{5} - 18 q^{7} - 20 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(155, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
155.2.r.a	$155$	$2$	155.r	155.r	$20$	$112$	$14$	$1.238$		None		$4$	$0$	\(-6\)	\(-10\)	\(-16\)	\(-18\)		$\mathrm{SU}(2)[C_{20}]$