Space of modular forms of level 63, weight 3, and Character 63.k

• Label: 63.3.k
• Level: $63$
• Weight: $3$
• Character orbit: 63.k
• Rep. character: $\chi_{63}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(63, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	28	28	0
Eisenstein series	8	8	0

Trace form

28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9 - 6 * q^10 - 14 * q^11 - 3 * q^12 + 15 * q^13 - 11 * q^14 - 18 * q^15 - 27 * q^16 - 33 * q^17 + 33 * q^18 - 6 * q^19 + 108 * q^20 + 12 * q^21 - 10 * q^22 - 68 * q^23 + 42 * q^24 - 62 * q^25 + 54 * q^26 - 81 * q^27 - 16 * q^28 + 70 * q^29 - 6 * q^30 + 45 * q^31 + 153 * q^32 - 114 * q^33 + 12 * q^34 + 18 * q^35 - 174 * q^36 + 9 * q^37 - 120 * q^39 - 234 * q^41 - 51 * q^42 + 30 * q^43 + 51 * q^44 + 276 * q^45 - 22 * q^46 - 111 * q^47 + 147 * q^48 + 34 * q^49 + 241 * q^50 - 6 * q^51 + 148 * q^53 + 378 * q^54 - 412 * q^56 + 189 * q^57 - 34 * q^58 + 42 * q^59 + 456 * q^60 + 120 * q^61 - 222 * q^63 - 48 * q^64 + 114 * q^65 - 447 * q^66 - 34 * q^67 + 78 * q^69 + 264 * q^70 - 350 * q^71 - 339 * q^72 - 6 * q^73 - 718 * q^74 - 123 * q^75 + 72 * q^76 - 32 * q^77 - 375 * q^78 - 82 * q^79 - 609 * q^80 - 3 * q^81 - 18 * q^82 + 738 * q^83 + 609 * q^84 + 3 * q^85 - 34 * q^86 + 3 * q^87 - 50 * q^88 + 21 * q^89 - 543 * q^90 + 39 * q^91 + 288 * q^92 + 252 * q^93 - 3 * q^94 + 507 * q^95 - 582 * q^96 - 57 * q^97 + 811 * q^98 - 162 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(63, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.3.k.a	$63$	$3$	63.k	63.k	$6$	$28$	$14$	$1.717$		None		✓	✓	✓	63.3.k.a	$2$	$0$	\(1\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$