Space of modular forms of level 54, weight 2, and trivial character

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

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	54.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(18\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(54))\).

	Total	New	Old
Modular forms	15	2	13
Cusp forms	4	2	2
Eisenstein series	11	0	11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	Fricke	Dim
\(+\)	\(-\)	$-$	\(1\)
\(-\)	\(+\)	$-$	\(1\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(2\)

Trace form

\( 2 q + 2 q^{4} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(54))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3
54.2.a.a	$54$	$2$	54.a	1.a	$1$	$1$	$1$	$0.431$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-q^{7}-q^{8}-3q^{10}+\cdots\)
54.2.a.b	$54$	$2$	54.a	1.a	$1$	$1$	$1$	$0.431$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(54))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(54)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)