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

• Label: 171.3.c
• Level: $171$
• Weight: $3$
• Character orbit: 171.c
• Rep. character: $\chi_{171}(37,\cdot)$
• Character field: $\Q$
• Dimension: $15$
• Newform subspaces: $6$
• Sturm bound: $60$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(60\)
Trace bound:			\(4\)
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	44	17	27
Cusp forms	36	15	21
Eisenstein series	8	2	6

Trace form

\( 15 q - 22 q^{4} + 3 q^{5} + q^{7} + O(q^{10}) \)

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.c.a	$171$	$3$	171.c	19.b	$2$	$1$	$1$	$4.659$	\(\Q\)	\(\Q(\sqrt{-19}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(9\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}+9q^{5}-5q^{7}-3q^{11}+2^{4}q^{16}+\cdots\)
171.3.c.b	$171$	$3$	171.c	19.b	$2$	$2$	$2$	$4.659$	\(\Q(\sqrt{-13}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-9q^{4}-4q^{5}-5q^{7}-5\beta q^{8}+\cdots\)
171.3.c.c	$171$	$3$	171.c	19.b	$2$	$2$	$2$	$4.659$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(-20\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}+q^{4}-4q^{5}-10q^{7}-5\zeta_{6}q^{8}+\cdots\)
171.3.c.d	$171$	$3$	171.c	19.b	$2$	$2$	$2$	$4.659$	\(\Q(\sqrt{19}) \)	\(\Q(\sqrt{-19}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}+\beta q^{5}+5q^{7}-5\beta q^{11}+2^{4}q^{16}+\cdots\)
171.3.c.e	$171$	$3$	171.c	19.b	$2$	$4$	$4$	$4.659$	\(\Q(\sqrt{-7}, \sqrt{10})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-3q^{4}+\beta _{2}q^{5}-2q^{7}-\beta _{1}q^{8}+\cdots\)
171.3.c.f	$171$	$3$	171.c	19.b	$2$	$4$	$4$	$4.659$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(0\)	\(10\)	\(34\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(3-\beta _{2})q^{5}+\cdots\)

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

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