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

• Label: 71.5.e
• Level: $71$
• Weight: $5$
• Character orbit: 71.e
• Rep. character: $\chi_{71}(14,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $92$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	71.e (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 71 \)
Character field:			\(\Q(\zeta_{10})\)
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	100	100	0
Cusp forms	92	92	0
Eisenstein series	8	8	0

Trace form

\( 92 q + 6 q^{2} - 13 q^{3} - 170 q^{4} - 9 q^{5} - 70 q^{6} - 5 q^{7} + 329 q^{8} - 742 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
71.5.e.a	$71$	$5$	71.e	71.e	$10$	$92$	$23$	$7.339$		None		✓	✓	✓	71.5.e.a	$2$	$0$	\(6\)	\(-13\)	\(-9\)	\(-5\)		$\mathrm{SU}(2)[C_{10}]$