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

• Label: 171.2.u
• Level: $171$
• Weight: $2$
• Character orbit: 171.u
• Rep. character: $\chi_{171}(28,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $42$
• Newform subspaces: $5$
• Sturm bound: $40$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(40\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	144	54	90
Cusp forms	96	42	54
Eisenstein series	48	12	36

Trace form

\( 42 q + 6 q^{2} - 12 q^{4} + 6 q^{5} - 6 q^{8} + O(q^{10}) \)

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.u.a	$171$	$2$	171.u	19.e	$9$	$6$	$1$	$1.365$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(-3\)	\(0\)	\(6\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{2}+(-1+\cdots)q^{4}+\cdots\)
171.2.u.b	$171$	$2$	171.u	19.e	$9$	$6$	$1$	$1.365$	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{9}]$	\(q-2\zeta_{18}^{2}q^{4}+(3\zeta_{18}-\zeta_{18}^{2}-2\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)
171.2.u.c	$171$	$2$	171.u	19.e	$9$	$6$	$1$	$1.365$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(6\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\zeta_{18}+\zeta_{18}^{2})q^{2}+(1-2\zeta_{18}+\cdots)q^{4}+\cdots\)
171.2.u.d	$171$	$2$	171.u	19.e	$9$	$12$	$2$	$1.365$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{1}q^{2}+(-1+2\beta _{6}-\beta _{7}-\beta _{9})q^{4}+\cdots\)
171.2.u.e	$171$	$2$	171.u	19.e	$9$	$12$	$2$	$1.365$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(3\)	\(0\)	\(-6\)	\(-9\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1+\beta _{1}+\beta _{2}-\beta _{5}+\beta _{9})q^{2}+(-1+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(171, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)