Space of modular forms of level 637, weight 2, and Character 637.ch

• Label: 637.2.ch
• Level: $637$
• Weight: $2$
• Character orbit: 637.ch
• Rep. character: $\chi_{637}(24,\cdot)$
• Character field: $\Q(\zeta_{84})$
• Dimension: $1512$
• Newform subspaces: $1$
• Sturm bound: $130$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.ch (of order \(84\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 637 \)
Character field:			\(\Q(\zeta_{84})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(130\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(637, [\chi])\).

	Total	New	Old
Modular forms	1608	1608	0
Cusp forms	1512	1512	0
Eisenstein series	96	96	0

Trace form

\( 1512 q - 26 q^{2} - 14 q^{3} - 36 q^{4} - 22 q^{5} - 40 q^{6} - 30 q^{7} - 24 q^{8} + 222 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(637, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
637.2.ch.a	$637$	$2$	637.ch	637.bh	$84$	$1512$	$63$	$5.086$		None		$2$	$0$	\(-26\)	\(-14\)	\(-22\)	\(-30\)		$\mathrm{SU}(2)[C_{84}]$