Space of modular forms of level 54, weight 2, and Character 54.e

• Label: 54.2.e
• Level: $54$
• Weight: $2$
• Character orbit: 54.e
• Rep. character: $\chi_{54}(7,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(18\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(54, [\chi])\).

	Total	New	Old
Modular forms	66	18	48
Cusp forms	42	18	24
Eisenstein series	24	0	24

Trace form

18 * q - 6 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 15 * q^11 - 3 * q^12 - 6 * q^14 - 18 * q^15 - 12 * q^17 + 6 * q^18 + 12 * q^20 + 24 * q^21 - 9 * q^22 + 24 * q^23 - 18 * q^25 + 36 * q^26 + 27 * q^27 + 30 * q^29 + 36 * q^30 - 18 * q^31 + 27 * q^33 - 9 * q^34 + 6 * q^35 + 6 * q^36 - 12 * q^38 - 42 * q^39 - 15 * q^41 - 24 * q^42 - 9 * q^43 - 6 * q^44 - 6 * q^48 - 18 * q^49 - 36 * q^50 - 24 * q^53 - 36 * q^54 - 6 * q^56 - 9 * q^57 + 6 * q^59 - 18 * q^60 - 18 * q^61 - 24 * q^62 - 6 * q^63 - 9 * q^64 + 6 * q^65 + 27 * q^67 - 12 * q^68 + 18 * q^69 + 36 * q^70 + 24 * q^71 + 24 * q^72 - 18 * q^73 + 30 * q^74 + 12 * q^75 + 18 * q^76 + 42 * q^77 + 36 * q^78 + 72 * q^79 + 12 * q^80 + 72 * q^85 + 27 * q^86 + 36 * q^87 + 18 * q^88 - 3 * q^89 + 18 * q^90 - 18 * q^91 + 6 * q^92 - 6 * q^93 + 36 * q^94 + 6 * q^95 + 6 * q^96 + 27 * q^97 - 15 * q^98 - 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(54, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
54.2.e.a	$54$	$2$	54.e	27.e	$9$	$6$	$1$	$0.431$	\(\Q(\zeta_{18})\)	None		✓			54.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\zeta_{18}q^{2}+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+\cdots\)
54.2.e.b	$54$	$2$	54.e	27.e	$9$	$12$	$2$	$0.431$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		54.2.e.b	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{4}+\beta _{6})q^{2}-\beta _{11}q^{3}+\beta _{3}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

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