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

• Label: 63.4.f
• Level: $63$
• Weight: $4$
• Character orbit: 63.f
• Rep. character: $\chi_{63}(22,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $36$
• Newform subspaces: $3$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	52	36	16
Cusp forms	44	36	8
Eisenstein series	8	0	8

Trace form

36 * q + 4 * q^2 + 2 * q^3 - 72 * q^4 + 8 * q^5 + 10 * q^6 - 108 * q^8 - 34 * q^9 + 134 * q^11 + 268 * q^12 + 56 * q^14 + 20 * q^15 - 288 * q^16 - 228 * q^17 - 470 * q^18 + 180 * q^19 - 26 * q^20 - 56 * q^21 - 36 * q^22 + 96 * q^23 - 366 * q^24 - 594 * q^25 + 1864 * q^26 + 704 * q^27 + 20 * q^29 + 40 * q^30 - 36 * q^31 + 266 * q^32 - 610 * q^33 + 576 * q^34 - 560 * q^35 + 952 * q^36 - 144 * q^37 - 1016 * q^38 - 832 * q^39 + 180 * q^40 - 326 * q^41 + 140 * q^42 + 342 * q^43 - 464 * q^44 + 308 * q^45 + 72 * q^46 - 12 * q^47 - 476 * q^48 - 882 * q^49 - 610 * q^50 - 1518 * q^51 - 918 * q^52 - 240 * q^53 + 1918 * q^54 - 792 * q^55 + 672 * q^56 + 158 * q^57 - 594 * q^58 + 678 * q^59 - 68 * q^60 + 1848 * q^62 - 476 * q^63 + 4212 * q^64 + 1640 * q^65 + 3166 * q^66 + 1386 * q^67 - 1146 * q^68 + 1200 * q^69 - 3744 * q^71 - 1926 * q^72 + 2484 * q^73 + 2076 * q^74 - 5570 * q^75 - 2196 * q^76 + 616 * q^77 + 4 * q^78 - 468 * q^79 - 4616 * q^80 - 2170 * q^81 - 7236 * q^82 - 1644 * q^83 + 2282 * q^84 + 1296 * q^85 + 3782 * q^86 + 1916 * q^87 + 1656 * q^88 + 5600 * q^89 - 3416 * q^90 + 504 * q^91 - 3726 * q^92 + 4332 * q^93 + 3006 * q^94 + 380 * q^95 - 280 * q^96 + 1998 * q^97 - 392 * q^98 + 4472 * 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.f.a	$63$	$4$	63.f	9.c	$3$	$2$	$1$	$3.717$	\(\Q(\sqrt{-3}) \)	None		✓			63.4.f.a	$2$	$0$	\(1\)	\(-9\)	\(14\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-6+3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
63.4.f.b	$63$	$4$	63.f	9.c	$3$	$16$	$8$	$3.717$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			63.4.f.b	$2$	$0$	\(-3\)	\(2\)	\(-30\)	\(56\)	$2^{2}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-\beta _{3}-\beta _{7})q^{3}+(5\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\)
63.4.f.c	$63$	$4$	63.f	9.c	$3$	$18$	$9$	$3.717$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓	✓		63.4.f.c	$2$	$0$	\(6\)	\(9\)	\(24\)	\(-63\)	$3^{10}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2}-\beta _{3}-\beta _{5})q^{2}+(1+\beta _{8})q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(63, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)