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

• Label: 63.3.n
• Level: $63$
• Weight: $3$
• Character orbit: 63.n
• Rep. character: $\chi_{63}(2,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

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

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 - 3 * q^2 - q^3 + 25 * q^4 - 8 * q^6 - 2 * q^7 - 7 * q^9 + 6 * q^10 + 19 * q^12 - 7 * q^13 - 39 * q^14 + 8 * q^15 - 35 * q^16 - 27 * q^17 - 83 * q^18 - 16 * q^19 + 6 * q^20 - 8 * q^21 + 6 * q^22 + 78 * q^24 - 62 * q^25 - 84 * q^26 + 65 * q^27 - 8 * q^28 - 114 * q^29 + 94 * q^30 + 17 * q^31 - 45 * q^32 + 104 * q^33 - 6 * q^34 + 30 * q^35 - 158 * q^36 - 13 * q^37 + 134 * q^39 + 96 * q^40 - 78 * q^41 - 145 * q^42 - 34 * q^43 + 327 * q^44 + 206 * q^45 + 18 * q^46 + 105 * q^47 + 169 * q^48 - 62 * q^49 + 357 * q^50 - 78 * q^51 - 34 * q^52 - 108 * q^53 - 404 * q^54 + 66 * q^55 + 450 * q^56 + 167 * q^57 - 66 * q^58 + 42 * q^59 - 32 * q^60 + 56 * q^61 + 484 * q^63 - 32 * q^64 - 372 * q^65 - 791 * q^66 - 34 * q^67 - 252 * q^69 + 150 * q^70 - 255 * q^72 - 100 * q^73 - 323 * q^75 + 134 * q^76 - 642 * q^77 - 197 * q^78 + 50 * q^79 + 3 * q^80 - 139 * q^81 - 6 * q^82 + 354 * q^83 - 739 * q^84 - 57 * q^85 + 17 * q^87 + 174 * q^88 - 477 * q^89 + 247 * q^90 + 107 * q^91 - 1092 * q^92 + 348 * q^93 - 183 * q^94 + 507 * q^95 + 1412 * q^96 + 17 * q^97 + 123 * q^98 - 184 * 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.n.a	$63$	$3$	63.n	63.n	$6$	$6$	$3$	$1.717$	6.0.63369648.1	None		✓			63.3.j.a	$2$	$0$	\(3\)	\(-9\)	\(0\)	\(-5\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{5})q^{2}+3\beta _{2}q^{3}+(\beta _{1}-4\beta _{2}+\cdots)q^{4}+\cdots\)
63.3.n.b	$63$	$3$	63.n	63.n	$6$	$22$	$11$	$1.717$		None		✓	✓		63.3.j.b	$2$	$0$	\(-6\)	\(8\)	\(0\)	\(3\)		$\mathrm{SU}(2)[C_{6}]$