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

• Label: 637.2.bp
• Level: $637$
• Weight: $2$
• Character orbit: 637.bp
• Rep. character: $\chi_{637}(88,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $756$
• 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.bp (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 637 \)
Character field:			\(\Q(\zeta_{42})\)
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	804	804	0
Cusp forms	756	756	0
Eisenstein series	48	48	0

Trace form

\( 756 q - 18 q^{2} - 11 q^{3} - 68 q^{4} - 15 q^{6} - 19 q^{7} - 121 q^{9} + O(q^{10}) \)

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.bp.a	$637$	$2$	637.bp	637.ap	$42$	$756$	$63$	$5.086$		None		$2$	$0$	\(-18\)	\(-11\)	\(0\)	\(-19\)		$\mathrm{SU}(2)[C_{42}]$