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

• Label: 83.7.b
• Level: $83$
• Weight: $7$
• Character orbit: 83.b
• Rep. character: $\chi_{83}(82,\cdot)$
• Character field: $\Q$
• Dimension: $41$
• Newform subspaces: $3$
• Sturm bound: $49$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 83 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	83.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 83 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(49\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	43	43	0
Cusp forms	41	41	0
Eisenstein series	2	2	0

Trace form

\( 41 q + 18 q^{3} - 1150 q^{4} + 262 q^{7} + 11255 q^{9} + O(q^{10}) \)

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.b.a	$83$	$7$	83.b	83.b	$2$	$1$	$1$	$19.094$	\(\Q\)	\(\Q(\sqrt{-83}) \)	✓	$2$	$0$	\(0\)	\(-29\)	\(0\)	\(-61\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-29q^{3}+2^{6}q^{4}-61q^{7}+112q^{9}+\cdots\)
83.7.b.b	$83$	$7$	83.b	83.b	$2$	$2$	$2$	$19.094$	\(\Q(\sqrt{249}) \)	\(\Q(\sqrt{-83}) \)	✓	$2$	$0$	\(0\)	\(29\)	\(0\)	\(61\)	$5$	$\mathrm{U}(1)[D_{2}]$	\(q+(15+\beta )q^{3}+2^{6}q^{4}+(23-15\beta )q^{7}+\cdots\)
83.7.b.c	$83$	$7$	83.b	83.b	$2$	$38$	$38$	$19.094$		None		$2$	$0$	\(0\)	\(18\)	\(0\)	\(262\)		$\mathrm{SU}(2)[C_{2}]$