Space of modular forms of level 63, weight 7, and Character 63.j

• Label: 63.7.j
• Level: $63$
• Weight: $7$
• Character orbit: 63.j
• Rep. character: $\chi_{63}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	63.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(63, [\chi])\).

	Total	New	Old
Modular forms	100	100	0
Cusp forms	92	92	0
Eisenstein series	8	8	0

Trace form

92 * q - q^3 - 2818 * q^4 - 3 * q^5 - 164 * q^6 - 121 * q^7 - 817 * q^9 + 126 * q^10 + 861 * q^11 - 4778 * q^12 + 838 * q^13 - 2676 * q^14 + 8093 * q^15 + 82046 * q^16 + 9072 * q^17 - 14804 * q^18 + 3358 * q^19 + 186 * q^20 - 2237 * q^21 + 126 * q^22 - 8211 * q^23 - 21858 * q^24 + 118751 * q^25 - 30048 * q^26 - 6640 * q^27 + 11324 * q^28 + 38550 * q^29 - 14495 * q^30 - 36962 * q^31 + 65741 * q^33 - 66 * q^34 + 65445 * q^35 + 90238 * q^36 - 9242 * q^37 - 273669 * q^38 + 229010 * q^39 - 23688 * q^40 - 155742 * q^41 + 478616 * q^42 + 43678 * q^43 - 561171 * q^44 + 92201 * q^45 + 67662 * q^46 - 9311 * q^48 + 69431 * q^49 + 195477 * q^50 - 738627 * q^51 - 115583 * q^52 - 434160 * q^53 + 565957 * q^54 + 228306 * q^55 + 372144 * q^56 - 137098 * q^57 + 159393 * q^58 - 1159007 * q^60 - 118610 * q^61 - 1068920 * q^63 - 2105224 * q^64 - 858368 * q^66 + 517438 * q^67 - 1927620 * q^68 + 26373 * q^69 + 642159 * q^70 + 2364882 * q^72 - 399842 * q^73 + 2924211 * q^74 + 42391 * q^75 - 425858 * q^76 - 2693955 * q^77 - 59693 * q^78 + 495622 * q^79 + 2698917 * q^80 - 859681 * q^81 - 66 * q^82 - 2305806 * q^83 - 1470727 * q^84 - 429627 * q^85 + 2640273 * q^86 + 384269 * q^87 - 270207 * q^88 + 1800036 * q^89 + 7451227 * q^90 + 63694 * q^91 + 3114744 * q^92 - 672501 * q^93 - 2946882 * q^94 + 6511211 * q^96 + 351118 * q^97 + 5868237 * q^98 - 3781939 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(63, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.7.j.a	$63$	$7$	63.j	63.j	$6$	$92$	$46$	$14.493$		None		✓	✓	✓	63.7.j.a	$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(-121\)		$\mathrm{SU}(2)[C_{6}]$