Space of modular forms of level 177, weight 2, and Character 177.d

• Label: 177.2.d
• Level: $177$
• Weight: $2$
• Character orbit: 177.d
• Rep. character: $\chi_{177}(176,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 177 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(177, [\chi])\).

	Total	New	Old
Modular forms	22	22	0
Cusp forms	18	18	0
Eisenstein series	4	4	0

Trace form

\( 18 q - 2 q^{3} + 12 q^{4} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(177, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
177.2.d.a	$177$	$2$	177.d	177.d	$2$	$6$	$6$	$1.413$	6.0.19298288.1	None		$2$	$0$	\(-4\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{1}+\beta _{2}+\beta _{5})q^{2}-\beta _{1}q^{3}+\cdots\)
177.2.d.b	$177$	$2$	177.d	177.d	$2$	$6$	$6$	$1.413$	6.0.149721291.1	\(\Q(\sqrt{-59}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}-2q^{4}+(\beta _{2}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
177.2.d.c	$177$	$2$	177.d	177.d	$2$	$6$	$6$	$1.413$	6.0.19298288.1	None		$2$	$0$	\(4\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1}-\beta _{2}-\beta _{5})q^{2}-\beta _{1}q^{3}+(2+\cdots)q^{4}+\cdots\)