Space of modular forms of level 54, weight 4, and Character 54.c

• Label: 54.4.c
• Level: $54$
• Weight: $4$
• Character orbit: 54.c
• Rep. character: $\chi_{54}(19,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	54.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(54, [\chi])\).

	Total	New	Old
Modular forms	66	6	60
Cusp forms	42	6	36
Eisenstein series	24	0	24

Trace form

6 * q - 2 * q^2 - 12 * q^4 - 18 * q^5 + 12 * q^7 + 16 * q^8 - 39 * q^11 - 24 * q^13 - 100 * q^14 - 48 * q^16 + 78 * q^17 + 210 * q^19 - 72 * q^20 - 18 * q^22 + 264 * q^23 - 219 * q^25 + 392 * q^26 - 96 * q^28 + 348 * q^29 - 6 * q^31 - 32 * q^32 + 90 * q^34 - 1332 * q^35 + 192 * q^37 - 322 * q^38 + 207 * q^41 + 129 * q^43 + 312 * q^44 + 504 * q^46 + 660 * q^47 - 585 * q^49 - 614 * q^50 - 96 * q^52 - 528 * q^53 - 1404 * q^55 - 400 * q^56 + 252 * q^58 + 327 * q^59 + 858 * q^61 + 1664 * q^62 + 384 * q^64 - 414 * q^65 + 1587 * q^67 - 156 * q^68 + 216 * q^70 + 312 * q^71 - 258 * q^73 - 856 * q^74 - 420 * q^76 - 708 * q^77 - 1482 * q^79 + 576 * q^80 - 2916 * q^82 + 138 * q^83 + 108 * q^85 + 86 * q^86 - 72 * q^88 + 3084 * q^89 + 2508 * q^91 + 1056 * q^92 + 612 * q^94 + 2016 * q^95 + 1029 * q^97 - 2604 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(54, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
54.4.c.a	$54$	$4$	54.c	9.c	$3$	$2$	$1$	$3.186$	\(\Q(\sqrt{-3}) \)	None					18.4.c.a	$2$	$0$	\(2\)	\(0\)	\(-9\)	\(31\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-9\zeta_{6}q^{5}+\cdots\)
54.4.c.b	$54$	$4$	54.c	9.c	$3$	$4$	$2$	$3.186$	\(\Q(\sqrt{-3}, \sqrt{-35})\)	None			✓		18.4.c.b	$2$	$0$	\(-4\)	\(0\)	\(-9\)	\(-19\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{1}q^{2}+(-4-4\beta _{1})q^{4}+(-4-4\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)