Space of modular forms of level 37, weight 8, and Character 37.c

• Label: 37.8.c
• Level: $37$
• Weight: $8$
• Character orbit: 37.c
• Rep. character: $\chi_{37}(10,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $42$
• Newform subspaces: $1$
• Sturm bound: $25$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(25\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(37, [\chi])\).

	Total	New	Old
Modular forms	46	46	0
Cusp forms	42	42	0
Eisenstein series	4	4	0

Trace form

\( 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(37, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.8.c.a	$37$	$8$	37.c	37.c	$3$	$42$	$21$	$11.558$		None		✓	✓	✓	37.8.c.a	$2$	$0$	\(-16\)	\(-68\)	\(-337\)	\(-158\)		$\mathrm{SU}(2)[C_{3}]$