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

• Label: 637.2.bn
• Level: $637$
• Weight: $2$
• Character orbit: 637.bn
• Rep. character: $\chi_{637}(34,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $744$
• 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.bn (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 637 \)
Character field:			\(\Q(\zeta_{28})\)
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	792	792	0
Cusp forms	744	744	0
Eisenstein series	48	48	0

Trace form

\( 744 q - 10 q^{2} - 28 q^{3} - 14 q^{5} - 14 q^{6} - 6 q^{7} - 18 q^{8} + 88 q^{9} + O(q^{10}) \)

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.bn.a	$637$	$2$	637.bn	637.an	$28$	$744$	$62$	$5.086$		None		$4$	$0$	\(-10\)	\(-28\)	\(-14\)	\(-6\)		$\mathrm{SU}(2)[C_{28}]$