Space of modular forms of level 54, weight 6, and Character 54.c

• Label: 54.6.c
• Level: $54$
• Weight: $6$
• Character orbit: 54.c
• Rep. character: $\chi_{54}(19,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $54$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(54\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(54, [\chi])\).

	Total	New	Old
Modular forms	102	10	92
Cusp forms	78	10	68
Eisenstein series	24	0	24

Trace form

10 * q + 4 * q^2 - 80 * q^4 + 108 * q^5 - 58 * q^7 - 128 * q^8 + 393 * q^11 + 362 * q^13 + 824 * q^14 - 1280 * q^16 - 3882 * q^17 - 1018 * q^19 + 1728 * q^20 - 948 * q^22 + 8706 * q^23 + 181 * q^25 - 14800 * q^26 + 1856 * q^28 + 9042 * q^29 - 3892 * q^31 + 1024 * q^32 - 3828 * q^34 - 432 * q^35 + 30344 * q^37 + 11084 * q^38 - 20403 * q^41 + 1469 * q^43 - 12576 * q^44 - 18960 * q^46 - 37878 * q^47 - 22413 * q^49 + 23788 * q^50 + 5792 * q^52 + 128712 * q^53 + 56160 * q^55 + 13184 * q^56 - 5016 * q^58 - 84921 * q^59 - 72916 * q^61 - 106624 * q^62 + 40960 * q^64 - 121284 * q^65 + 3767 * q^67 + 31056 * q^68 - 9936 * q^70 + 277368 * q^71 - 110842 * q^73 + 99056 * q^74 + 8144 * q^76 - 110202 * q^77 + 74276 * q^79 - 55296 * q^80 + 82440 * q^82 - 123396 * q^83 - 23112 * q^85 + 256988 * q^86 - 15168 * q^88 - 47532 * q^89 - 202712 * q^91 + 139296 * q^92 - 48120 * q^94 - 68472 * q^95 + 15983 * q^97 - 666408 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(54, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
54.6.c.a	$54$	$6$	54.c	9.c	$3$	$4$	$2$	$8.661$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					18.6.c.a	$2$	$0$	\(-8\)	\(0\)	\(54\)	\(74\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\beta _{1})q^{2}-2^{4}\beta _{1}q^{4}+(3^{3}\beta _{1}+\cdots)q^{5}+\cdots\)
54.6.c.b	$54$	$6$	54.c	9.c	$3$	$6$	$3$	$8.661$	6.0.\(\cdots\).3	None			✓		18.6.c.b	$2$	$0$	\(12\)	\(0\)	\(54\)	\(-132\)	$2^{2}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\beta _{1}q^{2}+(-2^{4}+2^{4}\beta _{1})q^{4}+(18+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)