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

• Label: 71.5.h
• Level: $71$
• Weight: $5$
• Character orbit: 71.h
• Rep. character: $\chi_{71}(7,\cdot)$
• Character field: $\Q(\zeta_{70})$
• Dimension: $552$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	71.h (of order \(70\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 71 \)
Character field:			\(\Q(\zeta_{70})\)
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	600	600	0
Cusp forms	552	552	0
Eisenstein series	48	48	0

Trace form

\( 552 q - 34 q^{2} - 50 q^{3} + 142 q^{4} - 12 q^{5} + 42 q^{6} - 23 q^{7} - 357 q^{8} + 469 q^{9} + O(q^{10}) \)

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.h.a	$71$	$5$	71.h	71.h	$70$	$552$	$23$	$7.339$		None		✓	✓	✓	71.5.h.a	$2$	$0$	\(-34\)	\(-50\)	\(-12\)	\(-23\)		$\mathrm{SU}(2)[C_{70}]$