Space of modular forms of level 172, weight 2, and Character 172.p

• Label: 172.2.p
• Level: $172$
• Weight: $2$
• Character orbit: 172.p
• Rep. character: $\chi_{172}(3,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $240$
• Newform subspaces: $1$
• Sturm bound: $44$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 172 = 2^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	172.p (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 172 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(44\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(172, [\chi])\).

	Total	New	Old
Modular forms	288	288	0
Cusp forms	240	240	0
Eisenstein series	48	48	0

Trace form

\( 240 q - 14 q^{2} - 12 q^{4} - 22 q^{5} - 4 q^{6} - 14 q^{8} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(172, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
172.2.p.a	$172$	$2$	172.p	172.p	$42$	$240$	$20$	$1.373$		None		$4$	$0$	\(-14\)	\(0\)	\(-22\)	\(0\)		$\mathrm{SU}(2)[C_{42}]$