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

• Label: 63.4.e
• Level: $63$
• Weight: $4$
• Character orbit: 63.e
• Rep. character: $\chi_{63}(37,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $18$
• Newform subspaces: $4$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	56	22	34
Cusp forms	40	18	22
Eisenstein series	16	4	12

Trace form

18 * q - 28 * q^4 + 15 * q^5 - 4 * q^7 - 72 * q^8 + 10 * q^10 + 15 * q^11 + 172 * q^13 + 228 * q^14 - 52 * q^16 + 111 * q^17 - 53 * q^19 - 816 * q^20 - 116 * q^22 - 27 * q^23 - 304 * q^25 + 438 * q^26 - 192 * q^28 + 372 * q^29 - 19 * q^31 + 888 * q^32 + 1404 * q^34 - 189 * q^35 + 209 * q^37 - 252 * q^38 - 612 * q^40 - 1908 * q^41 - 1152 * q^43 - 900 * q^44 - 594 * q^46 + 285 * q^47 - 462 * q^49 + 2364 * q^50 - 276 * q^52 + 1059 * q^53 + 2978 * q^55 - 480 * q^56 + 1936 * q^58 + 1023 * q^59 - 731 * q^61 - 4224 * q^62 - 408 * q^64 - 378 * q^65 - 1307 * q^67 + 2112 * q^68 + 2210 * q^70 + 912 * q^71 - 1987 * q^73 + 2388 * q^74 - 192 * q^76 - 723 * q^77 - 1233 * q^79 + 276 * q^80 - 2224 * q^82 - 4176 * q^83 + 570 * q^85 - 3534 * q^86 - 1596 * q^88 + 2343 * q^89 - 132 * q^91 + 240 * q^92 + 3570 * q^94 - 345 * q^95 + 5300 * q^97 + 4806 * q^98

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.e.a	$63$	$4$	63.e	7.c	$3$	$2$	$1$	$3.717$	\(\Q(\sqrt{-3}) \)	None					21.4.e.a	$2$	$0$	\(-3\)	\(0\)	\(-3\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3+3\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
63.4.e.b	$63$	$4$	63.e	7.c	$3$	$2$	$1$	$3.717$	\(\Q(\sqrt{-3}) \)	None					7.4.c.a	$2$	$0$	\(2\)	\(0\)	\(7\)	\(28\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}+4\zeta_{6}q^{4}+(7-7\zeta_{6})q^{5}+\cdots\)
63.4.e.c	$63$	$4$	63.e	7.c	$3$	$6$	$3$	$3.717$	6.0.9924270768.1	None					21.4.e.b	$2$	$0$	\(1\)	\(0\)	\(11\)	\(-13\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-8+\beta _{1}+\beta _{2}+8\beta _{4}+\beta _{5})q^{4}+\cdots\)
63.4.e.d	$63$	$4$	63.e	7.c	$3$	$8$	$4$	$3.717$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓		63.4.e.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{2}-\beta _{6})q^{4}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(63, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)