Space of modular forms of level 63, weight 8, and Character 63.h

• Label: 63.8.h
• Level: $63$
• Weight: $8$
• Character orbit: 63.h
• Rep. character: $\chi_{63}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $108$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	63.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(63, [\chi])\).

	Total	New	Old
Modular forms	116	116	0
Cusp forms	108	108	0
Eisenstein series	8	8	0

Trace form

108 * q - 2 * q^2 - q^3 + 6654 * q^4 - 499 * q^5 + 796 * q^6 - 84 * q^7 - 264 * q^8 - 2083 * q^9 - 258 * q^10 - 2953 * q^11 - 4262 * q^12 + 1845 * q^13 - 6064 * q^14 - 4756 * q^15 + 392958 * q^16 - 25695 * q^17 + 18628 * q^18 - 22344 * q^19 - 128642 * q^20 + 26395 * q^21 - 258 * q^22 + 24588 * q^23 + 9582 * q^24 - 718749 * q^25 - 184322 * q^26 - 108115 * q^27 - 37764 * q^28 - 46252 * q^29 - 368195 * q^30 + 215046 * q^31 - 896314 * q^32 - 508675 * q^33 + 126 * q^34 - 13856 * q^35 - 725486 * q^36 - 6219 * q^37 - 574289 * q^38 + 863855 * q^39 + 45102 * q^40 - 472490 * q^41 - 1455340 * q^42 - 48054 * q^43 - 763907 * q^44 - 1979983 * q^45 - 301266 * q^46 + 2767914 * q^47 + 3830059 * q^48 - 179010 * q^49 + 1454999 * q^50 - 1705518 * q^51 + 439809 * q^52 - 942852 * q^53 + 690229 * q^54 - 1333590 * q^55 - 960744 * q^56 - 4103881 * q^57 - 346383 * q^58 + 10263900 * q^59 + 1690429 * q^60 - 5446392 * q^61 + 17542716 * q^62 - 3666923 * q^63 + 20938488 * q^64 + 9110336 * q^65 + 8839522 * q^66 + 2503716 * q^67 - 3564510 * q^68 - 14621034 * q^69 + 5170071 * q^70 - 15030822 * q^71 + 10036926 * q^72 + 5865900 * q^73 - 10298901 * q^74 - 20070398 * q^75 - 5703426 * q^76 - 13731494 * q^77 + 18441853 * q^78 + 1098144 * q^79 - 22433777 * q^80 - 8145607 * q^81 + 126 * q^82 - 24302862 * q^83 + 10191035 * q^84 - 1239627 * q^85 - 8642455 * q^86 + 25559693 * q^87 + 2064129 * q^88 - 16002211 * q^89 + 28857805 * q^90 - 77007 * q^91 + 17446044 * q^92 - 1086678 * q^93 - 23171394 * q^94 + 8775674 * q^95 + 11149883 * q^96 - 3307419 * q^97 + 30910129 * q^98 - 27043330 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(63, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.8.h.a	$63$	$8$	63.h	63.h	$3$	$108$	$54$	$19.680$		None		✓	✓	✓	63.8.g.a	$2$	$0$	\(-2\)	\(-1\)	\(-499\)	\(-84\)		$\mathrm{SU}(2)[C_{3}]$