LMFDB - Space of modular forms of level 236, weight 2, and trivial character

Defining parameters

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(236))$.

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

$2$	$59$	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	59	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
236.2.a.a	$236$	$2$	236.a	1.a	$1$	$1$	$1$	$1.884$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots$
236.2.a.b	$236$	$2$	236.a	1.a	$1$	$1$	$1$	$1.884$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$3$	$-1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-q^{7}-2q^{9}+6q^{11}+\cdots$
236.2.a.c	$236$	$2$	236.a	1.a	$1$	$3$	$3$	$1.884$	3.3.321.1	None	✓	$1$	$0$	$0$	$0$	$-4$	$8$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{1})q^{5}+(3+\cdots)q^{7}+\cdots$

$ S_{2}^{\mathrm{old}}(\Gamma_0(236)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(59))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(118))$$^{\oplus 2}$

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\(2\)	\(59\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	$+$	\(1\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(4\)