Space of modular forms of level 83, weight 2, and Character 83.c

• Label: 83.2.c
• Level: $83$
• Weight: $2$
• Character orbit: 83.c
• Rep. character: $\chi_{83}(3,\cdot)$
• Character field: $\Q(\zeta_{41})$
• Dimension: $240$
• Newform subspaces: $1$
• Sturm bound: $14$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	83.c (of order \(41\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 83 \)
Character field:			\(\Q(\zeta_{41})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(14\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(83, [\chi])\).

	Total	New	Old
Modular forms	320	320	0
Cusp forms	240	240	0
Eisenstein series	80	80	0

Trace form

\( 240 q - 38 q^{2} - 37 q^{3} - 40 q^{4} - 35 q^{5} - 23 q^{6} - 33 q^{7} - 32 q^{8} - 29 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(83, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
83.2.c.a	$83$	$2$	83.c	83.c	$41$	$240$	$6$	$0.663$		None		$2$	$0$	\(-38\)	\(-37\)	\(-35\)	\(-33\)		$\mathrm{SU}(2)[C_{41}]$