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

• Label: 637.2.w
• Level: $637$
• Weight: $2$
• Character orbit: 637.w
• Rep. character: $\chi_{637}(92,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $336$
• Newform subspaces: $2$
• Sturm bound: $130$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.w (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 2 \)
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	396	336	60
Cusp forms	372	336	36
Eisenstein series	24	0	24

Trace form

336 * q - 56 * q^4 - 8 * q^5 + 16 * q^6 - 6 * q^7 - 12 * q^8 - 36 * q^9 - 20 * q^10 + 10 * q^11 + 50 * q^12 - 2 * q^13 + 48 * q^14 + 8 * q^15 - 56 * q^16 - 6 * q^17 - 20 * q^18 + 48 * q^19 + 16 * q^20 - 28 * q^21 + 16 * q^22 + 14 * q^23 - 56 * q^24 - 84 * q^25 - 6 * q^26 + 6 * q^27 - 42 * q^28 + 48 * q^29 - 52 * q^30 + 56 * q^31 + 40 * q^32 - 44 * q^33 + 56 * q^34 - 46 * q^35 - 16 * q^36 - 16 * q^37 - 38 * q^38 + 116 * q^40 - 16 * q^41 + 92 * q^42 - 36 * q^43 - 60 * q^44 + 82 * q^45 + 60 * q^46 - 28 * q^47 - 136 * q^48 - 28 * q^49 - 60 * q^50 - 44 * q^51 - 6 * q^52 + 8 * q^53 - 84 * q^54 + 98 * q^55 - 32 * q^56 - 22 * q^57 + 60 * q^58 - 48 * q^59 + 152 * q^60 - 48 * q^61 - 74 * q^62 - 86 * q^63 - 116 * q^64 + 110 * q^66 - 32 * q^67 - 168 * q^68 - 76 * q^69 - 104 * q^70 + 22 * q^71 + 66 * q^72 - 52 * q^73 - 116 * q^74 + 134 * q^75 + 54 * q^76 - 88 * q^77 + 50 * q^78 - 52 * q^79 + 132 * q^80 + 44 * q^81 - 140 * q^82 - 10 * q^83 + 110 * q^84 - 68 * q^85 + 48 * q^86 - 76 * q^87 + 54 * q^88 - 18 * q^89 - 142 * q^90 - 4 * q^91 - 52 * q^92 + 108 * q^93 + 44 * q^94 - 92 * q^95 - 10 * q^96 - 36 * q^97 - 104 * q^98 + 104 * q^99

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.w.a	$637$	$2$	637.w	49.e	$7$	$162$	$27$	$5.086$		None		✓			637.2.w.a	$2$	$0$	\(3\)	\(0\)	\(-4\)	\(-15\)		$\mathrm{SU}(2)[C_{7}]$
637.2.w.b	$637$	$2$	637.w	49.e	$7$	$174$	$29$	$5.086$		None		✓	✓		637.2.w.b	$2$	$0$	\(-3\)	\(0\)	\(-4\)	\(9\)		$\mathrm{SU}(2)[C_{7}]$

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

\( S_{2}^{\mathrm{old}}(637, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)