LMFDB - Space of modular forms of level 212, weight 2, and trivial character

Defining parameters

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(212))$.

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

$2$	$53$	Fricke	Dim
$-$	$+$	$-$	$4$
$-$	$-$	$+$	$1$
Plus space		$+$	$1$
Minus space		$-$	$4$

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	53	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
212.2.a.a	$212$	$2$	212.a	1.a	$1$	$1$	$1$	$1.693$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-2q^{7}-2q^{9}+2q^{11}+\cdots$
212.2.a.b	$212$	$2$	212.a	1.a	$1$	$1$	$1$	$1.693$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
212.2.a.c	$212$	$2$	212.a	1.a	$1$	$3$	$3$	$1.693$	3.3.756.1	None	✓	$1$	$0$	$0$	$-3$	$0$	$6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-\beta _{2}q^{5}+(2+\beta _{2})q^{7}+\cdots$

$ S_{2}^{\mathrm{old}}(\Gamma_0(212)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(53))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(106))$$^{\oplus 2}$

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\(2\)	\(53\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	$+$	\(1\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(4\)