Space of modular forms of level 71, weight 10, and Character 71.g

• Label: 71.10.g
• Level: $71$
• Weight: $10$
• Character orbit: 71.g
• Rep. character: $\chi_{71}(2,\cdot)$
• Character field: $\Q(\zeta_{35})$
• Dimension: $1272$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 71 \)
Character field:			\(\Q(\zeta_{35})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(71, [\chi])\).

	Total	New	Old
Modular forms	1320	1320	0
Cusp forms	1272	1272	0
Eisenstein series	48	48	0

Trace form

\( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(71, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
71.10.g.a	$71$	$10$	71.g	71.g	$35$	$1272$	$53$	$36.568$		None		$2$	$0$	\(-76\)	\(-395\)	\(-1610\)	\(-4827\)		$\mathrm{SU}(2)[C_{35}]$