Space of modular forms of level 71, weight 5, and Character 71.f

• Label: 71.5.f
• Level: $71$
• Weight: $5$
• Character orbit: 71.f
• Rep. character: $\chi_{71}(23,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $138$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	71.f (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 71 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(71, [\chi])\).

	Total	New	Old
Modular forms	150	150	0
Cusp forms	138	138	0
Eisenstein series	12	12	0

Trace form

\( 138 q - 11 q^{2} + 20 q^{3} - 187 q^{4} - 18 q^{5} + 93 q^{6} - 7 q^{7} - 123 q^{8} - 329 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(71, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
71.5.f.a	$71$	$5$	71.f	71.f	$14$	$138$	$23$	$7.339$		None		$2$	$0$	\(-11\)	\(20\)	\(-18\)	\(-7\)		$\mathrm{SU}(2)[C_{14}]$