Space of modular forms of level 63, weight 4, and Character 63.h

• Label: 63.4.h
• Level: $63$
• Weight: $4$
• Character orbit: 63.h
• Rep. character: $\chi_{63}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $44$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(63, [\chi])\).

	Total	New	Old
Modular forms	52	52	0
Cusp forms	44	44	0
Eisenstein series	8	8	0

Trace form

44 * q - 2 * q^2 - q^3 + 158 * q^4 - 19 * q^5 - 20 * q^6 - 7 * q^7 - 24 * q^8 + 11 * q^9 - 18 * q^10 + 5 * q^11 - 62 * q^12 - 14 * q^13 - 52 * q^14 + 119 * q^15 + 494 * q^16 - 162 * q^17 - 188 * q^18 + 58 * q^19 - 362 * q^20 - 59 * q^21 - 18 * q^22 - 93 * q^23 + 30 * q^24 - 349 * q^25 - 266 * q^26 + 272 * q^27 - 172 * q^28 + 248 * q^29 + 85 * q^30 - 122 * q^31 + 326 * q^32 + 77 * q^33 + 6 * q^34 + 289 * q^35 - 806 * q^36 - 86 * q^37 - 761 * q^38 - 256 * q^39 - 18 * q^40 - 692 * q^41 - 364 * q^42 - 86 * q^43 - 443 * q^44 + 527 * q^45 - 270 * q^46 + 2010 * q^47 - 1013 * q^48 + 317 * q^49 + 239 * q^50 + 1209 * q^51 - 335 * q^52 + 258 * q^53 + 577 * q^54 - 870 * q^55 - 1752 * q^56 + 566 * q^57 + 237 * q^58 + 3330 * q^59 + 1669 * q^60 - 878 * q^61 + 1812 * q^62 + 2872 * q^63 + 872 * q^64 + 1226 * q^65 + 1330 * q^66 - 590 * q^67 - 1374 * q^68 + 1389 * q^69 + 1251 * q^70 + 636 * q^71 - 5970 * q^72 - 338 * q^73 + 1119 * q^74 + 2737 * q^75 + 1006 * q^76 + 2269 * q^77 + 157 * q^78 - 266 * q^79 - 4817 * q^80 - 505 * q^81 + 6 * q^82 - 1356 * q^83 - 6013 * q^84 + 483 * q^85 - 3343 * q^86 - 5755 * q^87 + 369 * q^88 - 2200 * q^89 + 2665 * q^90 + 1552 * q^91 - 396 * q^92 - 129 * q^93 + 2382 * q^94 - 6166 * q^95 - 5941 * q^96 - 266 * q^97 + 3601 * q^98 - 5395 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(63, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.4.h.a	$63$	$4$	63.h	63.h	$3$	$44$	$22$	$3.717$		None		✓	✓	✓	63.4.g.a	$2$	$0$	\(-2\)	\(-1\)	\(-19\)	\(-7\)		$\mathrm{SU}(2)[C_{3}]$