Space of modular forms of level 41, weight 2, and Character 41.c

• Label: 41.2.c
• Level: $41$
• Weight: $2$
• Character orbit: 41.c
• Rep. character: $\chi_{41}(9,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $7$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	41.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(7\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(41, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

Trace form

\( 6 q - 4 q^{3} - 10 q^{4} + 2 q^{6} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(41, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
41.2.c.a	$41$	$2$	41.c	41.c	$4$	$6$	$3$	$0.327$	6.0.5089536.1	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots\)