Space of modular forms of level 171, weight 2, and Character 171.d

• Label: 171.2.d
• Level: $171$
• Weight: $2$
• Character orbit: 171.d
• Rep. character: $\chi_{171}(170,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $40$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(40\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(171, [\chi])\).

	Total	New	Old
Modular forms	24	8	16
Cusp forms	16	8	8
Eisenstein series	8	0	8

Trace form

\( 8 q + 4 q^{4} - 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(171, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
171.2.d.a	$171$	$2$	171.d	57.d	$2$	$4$	$4$	$1.365$	\(\Q(\sqrt{-2}, \sqrt{19})\)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{4}+\beta _{1}q^{5}+\beta _{3}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
171.2.d.b	$171$	$2$	171.d	57.d	$2$	$4$	$4$	$1.365$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+3q^{4}-\beta _{1}q^{5}-2q^{7}-\beta _{3}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(171, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(171, [\chi]) \cong \)