LMFDB - Space of modular forms of level 72, weight 2, and trivial character

Defining parameters

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(72))$.

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
$+$	$-$	$-$	$1$
Plus space		$+$	$0$
Minus space		$-$	$1$

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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
72.2.a.a	$72$	$2$	72.a	1.a	$1$	$1$	$1$	$0.575$	$\Q$	None	✓		✓	✓	24.2.a.a	$1$	$0$	$0$	$0$	$2$	$0$		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{11}-2q^{13}-2q^{17}-4q^{19}+\cdots$

$ S_{2}^{\mathrm{old}}(\Gamma_0(72)) \simeq $ $S_{2}^{\mathrm{new}}(\Gamma_0(24))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(36))$$^{\oplus 2}$

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Classical	Maass
Hilbert	Bianchi

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