Space of modular forms of level 54, weight 8, and Character 54.c

• Label: 54.8.c
• Level: $54$
• Weight: $8$
• Character orbit: 54.c
• Rep. character: $\chi_{54}(19,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(54, [\chi])\).

	Total	New	Old
Modular forms	138	14	124
Cusp forms	114	14	100
Eisenstein series	24	0	24

Trace form

14 * q - 8 * q^2 - 448 * q^4 - 108 * q^5 + 166 * q^7 + 1024 * q^8 - 8751 * q^11 + 3694 * q^13 - 2032 * q^14 - 28672 * q^16 + 81762 * q^17 - 46778 * q^19 - 6912 * q^20 + 35256 * q^22 + 41682 * q^23 - 181369 * q^25 + 263840 * q^26 - 21248 * q^28 - 522930 * q^29 + 144892 * q^31 - 32768 * q^32 - 88728 * q^34 + 2580768 * q^35 - 278696 * q^37 - 912808 * q^38 - 1697697 * q^41 - 384347 * q^43 + 1120128 * q^44 + 602016 * q^46 - 987342 * q^47 - 790863 * q^49 - 1324184 * q^50 + 236416 * q^52 - 66552 * q^53 + 1521936 * q^55 - 130048 * q^56 - 346128 * q^58 - 2885649 * q^59 + 4157908 * q^61 + 2344256 * q^62 + 3670016 * q^64 + 2113236 * q^65 - 6528545 * q^67 - 2616384 * q^68 - 1620864 * q^70 - 11239752 * q^71 + 13333186 * q^73 - 4648288 * q^74 + 1496896 * q^76 + 12102258 * q^77 - 10232468 * q^79 + 884736 * q^80 - 7620624 * q^82 + 22434636 * q^83 + 2938248 * q^85 + 1724696 * q^86 + 2256384 * q^88 - 49866420 * q^89 - 10938616 * q^91 + 2667648 * q^92 - 5792592 * q^94 + 48359376 * q^95 - 21483755 * q^97 + 28083408 * q^98

Decomposition of \(S_{8}^{\mathrm{new}}(54, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
54.8.c.a	$54$	$8$	54.c	9.c	$3$	$6$	$3$	$16.869$	6.0.\(\cdots\).1	None					18.8.c.a	$2$	$0$	\(24\)	\(0\)	\(-54\)	\(210\)	$2^{2}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{3}]$	\(q+8\beta _{1}q^{2}+(-2^{6}+2^{6}\beta _{1})q^{4}+(-18+\cdots)q^{5}+\cdots\)
54.8.c.b	$54$	$8$	54.c	9.c	$3$	$8$	$4$	$16.869$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None			✓		18.8.c.b	$2$	$0$	\(-32\)	\(0\)	\(-54\)	\(-44\)	$2^{4}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{3}]$	\(q-8\beta _{1}q^{2}+(-2^{6}+2^{6}\beta _{1})q^{4}+(-14+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)