LMFDB - Space of modular forms of level 112, weight 2, and trivial character

Defining parameters

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(112))$.

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

$2$	$7$	Fricke	Dim
$+$	$+$	$+$	$1$
$+$	$-$	$-$	$1$
$-$	$+$	$-$	$1$
Plus space		$+$	$1$
Minus space		$-$	$2$

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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
112.2.a.a	$112$	$2$	112.a	1.a	$1$	$1$	$1$	$0.894$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$-4$	$-1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{5}-q^{7}+q^{9}+8q^{15}+\cdots$
112.2.a.b	$112$	$2$	112.a	1.a	$1$	$1$	$1$	$0.894$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$2$	$1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-3q^{9}+4q^{11}+2q^{13}+\cdots$
112.2.a.c	$112$	$2$	112.a	1.a	$1$	$1$	$1$	$0.894$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$0$	$-1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{7}+q^{9}-4q^{13}+6q^{17}+\cdots$

$ S_{2}^{\mathrm{old}}(\Gamma_0(112)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(14))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(28))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(56))$$^{\oplus 2}$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

\(2\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	$-$	\(1\)
\(-\)	\(+\)	$-$	\(1\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(2\)