LMFDB - Space of modular forms of level 188, weight 2, and trivial character

Defining parameters

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(188))$.

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

$2$	$47$	Fricke	Dim
$-$	$+$	$-$	$2$
$-$	$-$	$+$	$2$
Plus space		$+$	$2$
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	47	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
188.2.a.a	$188$	$2$	188.a	1.a	$1$	$2$	$2$	$1.501$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-3$	$-2$	$-7$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-2+2\beta )q^{5}+(-4+\cdots)q^{7}+\cdots$
188.2.a.b	$188$	$2$	188.a	1.a	$1$	$2$	$2$	$1.501$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$0$	$1$	$0$	$5$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(3-\beta )q^{7}+\beta q^{9}+(2-2\beta )q^{11}+\cdots$

$ S_{2}^{\mathrm{old}}(\Gamma_0(188)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(47))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(94))$$^{\oplus 2}$

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Classical	Maass
Hilbert	Bianchi

\(2\)	\(47\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(2\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(2\)