Space of modular forms of level 54, weight 3, and Character 54.d

• Label: 54.3.d
• Level: $54$
• Weight: $3$
• Character orbit: 54.d
• Rep. character: $\chi_{54}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $27$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	54.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(27\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(54, [\chi])\).

	Total	New	Old
Modular forms	48	4	44
Cusp forms	24	4	20
Eisenstein series	24	0	24

Trace form

4 * q + 4 * q^4 + 18 * q^5 + 2 * q^7 - 18 * q^11 - 10 * q^13 - 36 * q^14 - 8 * q^16 - 40 * q^19 + 36 * q^20 - 12 * q^22 - 18 * q^23 + 4 * q^25 + 8 * q^28 - 18 * q^29 + 38 * q^31 + 24 * q^34 + 128 * q^37 + 72 * q^38 + 126 * q^41 - 46 * q^43 - 24 * q^46 - 54 * q^47 - 12 * q^49 + 20 * q^52 - 108 * q^55 - 72 * q^56 + 24 * q^58 - 126 * q^59 + 62 * q^61 - 32 * q^64 - 90 * q^65 - 106 * q^67 - 72 * q^68 - 108 * q^70 - 208 * q^73 - 72 * q^74 - 40 * q^76 + 90 * q^77 + 14 * q^79 + 144 * q^82 + 378 * q^83 + 108 * q^85 + 108 * q^86 + 24 * q^88 + 412 * q^91 - 36 * q^92 + 84 * q^94 - 180 * q^95 + 14 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(54, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
54.3.d.a	$54$	$3$	54.d	9.d	$6$	$4$	$2$	$1.471$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None			✓	✓	18.3.d.a	$2$	$0$	\(0\)	\(0\)	\(18\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(6-3\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)