Space of modular forms of level 83, weight 7, and Character 83.d

• Label: 83.7.d
• Level: $83$
• Weight: $7$
• Character orbit: 83.d
• Rep. character: $\chi_{83}(2,\cdot)$
• Character field: $\Q(\zeta_{82})$
• Dimension: $1640$
• Newform subspaces: $1$
• Sturm bound: $49$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 83 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	83.d (of order \(82\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 83 \)
Character field:			\(\Q(\zeta_{82})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(49\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(83, [\chi])\).

	Total	New	Old
Modular forms	1720	1720	0
Cusp forms	1640	1640	0
Eisenstein series	80	80	0

Trace form

\( 1640 q - 41 q^{2} - 59 q^{3} + 1109 q^{4} - 41 q^{5} - 41 q^{6} - 303 q^{7} - 41 q^{8} - 11296 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(83, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
83.7.d.a	$83$	$7$	83.d	83.d	$82$	$1640$	$41$	$19.094$		None		$2$	$0$	\(-41\)	\(-59\)	\(-41\)	\(-303\)		$\mathrm{SU}(2)[C_{82}]$