Space of modular forms of level 171, weight 3, and Character 171.p

• Label: 171.3.p
• Level: $171$
• Weight: $3$
• Character orbit: 171.p
• Rep. character: $\chi_{171}(46,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $30$
• Newform subspaces: $6$
• Sturm bound: $60$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(60\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(171, [\chi])\).

	Total	New	Old
Modular forms	88	34	54
Cusp forms	72	30	42
Eisenstein series	16	4	12

Trace form

\( 30 q + 3 q^{2} + 25 q^{4} - 16 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(171, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
171.3.p.a	$171$	$3$	171.p	19.d	$6$	$2$	$1$	$4.659$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-3\)	\(0\)	\(-4\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-4+4\zeta_{6})q^{5}+\cdots\)
171.3.p.b	$171$	$3$	171.p	19.d	$6$	$2$	$1$	$4.659$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(3\)	\(0\)	\(4\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(4-4\zeta_{6})q^{5}+\cdots\)
171.3.p.c	$171$	$3$	171.p	19.d	$6$	$6$	$3$	$4.659$	6.0.92607408.1	None		$2$	$0$	\(-3\)	\(0\)	\(-4\)	\(-22\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{2}+(1+\beta _{1}+2\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
171.3.p.d	$171$	$3$	171.p	19.d	$6$	$6$	$3$	$4.659$	6.0.6967728.1	None		$2$	$0$	\(3\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{5})q^{2}+(-2\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
171.3.p.e	$171$	$3$	171.p	19.d	$6$	$6$	$3$	$4.659$	6.0.6967728.1	None		$2$	$0$	\(3\)	\(0\)	\(2\)	\(26\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
171.3.p.f	$171$	$3$	171.p	19.d	$6$	$8$	$4$	$4.659$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-40\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(3\beta _{2}+\beta _{4}+2\beta _{6})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(171, [\chi])\) into lower level spaces

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