LMFDB - Space of modular forms of level 81, weight 2, and trivial character

Defining parameters

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(81))$.

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

$3$	Total			Cusp			Eisenstein
$3$	All	New	Old	All	New	Old	All	New	Old
$+$	$6$	$2$	$4$	$1$	$0$	$1$	$5$	$2$	$3$
$-$	$9$	$4$	$5$	$3$	$2$	$1$	$6$	$2$	$4$

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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
81.2.a.a	$81$	$2$	81.a	1.a	$1$	$2$	$2$	$0.647$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	81.2.a.a	$2$	$0$	$0$	$0$	$0$	$4$		$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{5}+2q^{7}-\beta q^{8}+\cdots$

$ S_{2}^{\mathrm{old}}(\Gamma_0(81)) \simeq $ $S_{2}^{\mathrm{new}}(\Gamma_0(27))$$^{\oplus 2}$

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Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

\(3\)	Total			Cusp			Eisenstein
\(3\)	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(6\)	\(2\)	\(4\)	\(1\)	\(0\)	\(1\)	\(5\)	\(2\)	\(3\)
\(-\)	\(9\)	\(4\)	\(5\)	\(3\)	\(2\)	\(1\)	\(6\)	\(2\)	\(4\)