Space of modular forms of level 41, weight 6, and Character 41.f

• Label: 41.6.f
• Level: $41$
• Weight: $6$
• Character orbit: 41.f
• Rep. character: $\chi_{41}(4,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $64$
• Newform subspaces: $1$
• Sturm bound: $21$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	41.f (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(21\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(41, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	64	64	0
Eisenstein series	8	8	0

Trace form

\( 64 q - 11 q^{2} - 227 q^{4} - 37 q^{5} + 135 q^{6} - 5 q^{7} - 1208 q^{8} - 4342 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(41, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
41.6.f.a	$41$	$6$	41.f	41.f	$10$	$64$	$16$	$6.576$		None		✓	41.6.f.a	$2$	$0$	\(-11\)	\(0\)	\(-37\)	\(-5\)		$\mathrm{SU}(2)[C_{10}]$