Space of modular forms of level 54, weight 5, and Character 54.b

• Label: 54.5.b
• Level: $54$
• Weight: $5$
• Character orbit: 54.b
• Rep. character: $\chi_{54}(53,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $45$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	54.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(45\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(54, [\chi])\).

	Total	New	Old
Modular forms	42	6	36
Cusp forms	30	6	24
Eisenstein series	12	0	12

Trace form

\( 6 q - 48 q^{4} - 78 q^{7} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
54.5.b.a	$54$	$5$	54.b	3.b	$2$	$2$	$2$	$5.582$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-146\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-8q^{4}-12\beta q^{5}-73q^{7}-8\beta q^{8}+\cdots\)
54.5.b.b	$54$	$5$	54.b	3.b	$2$	$4$	$4$	$5.582$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(68\)	$2^{3}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}-8q^{4}+(\zeta_{8}-3\zeta_{8}^{2})q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(54, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)