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

• Label: 41.2.b
• Level: $41$
• Weight: $2$
• Character orbit: 41.b
• Rep. character: $\chi_{41}(40,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $7$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	41.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q\)
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	4	4	0
Cusp forms	2	2	0
Eisenstein series	2	2	0

Trace form

\( 2 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 6 q^{8} - 10 q^{9} + O(q^{10}) \)

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.b.a	$41$	$2$	41.b	41.b	$2$	$2$	$2$	$0.327$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta q^{3}-q^{4}+2q^{5}-\beta q^{6}-\beta q^{7}+\cdots\)