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

• Label: 637.2.bc
• Level: $637$
• Weight: $2$
• Character orbit: 637.bc
• Rep. character: $\chi_{637}(31,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $168$
• Newform subspaces: $3$
• Sturm bound: $130$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bc (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:			\(1\)
Distinguishing \(T_p\):			\(2\)

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 + 2 * q^2 + 12 * q^3 + 6 * q^5 - 8 * q^8 + 68 * q^9 + 14 * q^11 + 44 * q^15 + 52 * q^16 + 36 * q^18 - 12 * q^19 - 40 * q^22 + 12 * q^24 - 24 * q^26 - 88 * q^29 - 24 * q^31 + 20 * q^32 - 48 * q^33 - 20 * q^37 - 14 * q^39 + 132 * q^40 + 10 * q^44 + 24 * q^45 - 44 * q^46 - 30 * q^47 - 48 * q^50 - 36 * q^52 + 16 * q^53 - 78 * q^54 - 168 * q^57 - 2 * q^58 + 54 * q^59 + 36 * q^60 + 48 * q^61 - 12 * q^66 - 44 * q^67 + 48 * q^68 + 28 * q^71 - 158 * q^72 - 66 * q^73 - 148 * q^74 + 232 * q^78 + 52 * q^79 - 138 * q^80 - 44 * q^81 - 12 * q^85 - 58 * q^86 + 24 * q^87 + 60 * q^89 - 160 * q^92 - 30 * q^93 + 72 * q^94 + 42 * q^96

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
637.2.bc.a	$637$	$2$	637.bc	91.ab	$12$	$24$	$6$	$5.086$		None					91.2.i.a	$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
637.2.bc.b	$637$	$2$	637.bc	91.ab	$12$	$32$	$8$	$5.086$		None					91.2.bb.a	$4$	$0$	\(-2\)	\(12\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
637.2.bc.c	$637$	$2$	637.bc	91.ab	$12$	$112$	$28$	$5.086$		None		✓	✓		637.2.i.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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