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

• Label: 637.2.bd
• Level: $637$
• Weight: $2$
• Character orbit: 637.bd
• Rep. character: $\chi_{637}(97,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $168$
• Newform subspaces: $3$
• Sturm bound: $130$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bd (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(130\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	296	200	96
Cusp forms	232	168	64
Eisenstein series	64	32	32

Trace form

\( 168 q + 8 q^{2} + 12 q^{4} - 8 q^{8} + 68 q^{9} + O(q^{10}) \)

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.bd.a	$637$	$2$	637.bd	91.ac	$12$	$28$	$7$	$5.086$		None		$2$	$0$	\(4\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
637.2.bd.b	$637$	$2$	637.bd	91.ac	$12$	$28$	$7$	$5.086$		None		$2$	$0$	\(4\)	\(6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
637.2.bd.c	$637$	$2$	637.bd	91.ac	$12$	$112$	$28$	$5.086$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(637, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(637, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)