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

• Label: 172.2.d
• Level: $172$
• Weight: $2$
• Character orbit: 172.d
• Rep. character: $\chi_{172}(171,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 172 \)
Character field:			\(\Q\)
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	24	24	0
Cusp forms	20	20	0
Eisenstein series	4	4	0

Trace form

\( 20 q - 4 q^{4} - 6 q^{6} + 16 q^{9} + O(q^{10}) \)

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.d.a	$172$	$2$	172.d	172.d	$2$	$20$	$20$	$1.373$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{2}+\beta _{14}q^{3}+\beta _{6}q^{4}-\beta _{4}q^{5}+\cdots\)