Space of modular forms of level 176, weight 2, and Character 176.w

• Label: 176.2.w
• Level: $176$
• Weight: $2$
• Character orbit: 176.w
• Rep. character: $\chi_{176}(5,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $176$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	176.w (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 176 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(176, [\chi])\).

	Total	New	Old
Modular forms	208	208	0
Cusp forms	176	176	0
Eisenstein series	32	32	0

Trace form

\( 176 q - 6 q^{2} - 6 q^{3} - 10 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(176, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
176.2.w.a	$176$	$2$	176.w	176.w	$20$	$176$	$22$	$1.405$		None		$4$	$0$	\(-6\)	\(-6\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$