LMFDB - Space of modular forms of level 135, weight 2, and trivial character

Defining parameters

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(135))$.

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

$3$	$5$	Fricke	Dim
$+$	$+$	$+$	$1$
$+$	$-$	$-$	$3$
$-$	$+$	$-$	$2$
Plus space		$+$	$1$
Minus space		$-$	$5$

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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
135.2.a.a	$135$	$2$	135.a	1.a	$1$	$1$	$1$	$1.078$	$\Q$	None	✓	$1$	$1$	$-2$	$0$	$-1$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots$
135.2.a.b	$135$	$2$	135.a	1.a	$1$	$1$	$1$	$1.078$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$1$	$-3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots$
135.2.a.c	$135$	$2$	135.a	1.a	$1$	$2$	$2$	$1.078$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$-1$	$0$	$2$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+q^{5}+(2-2\beta )q^{7}+\cdots$
135.2.a.d	$135$	$2$	135.a	1.a	$1$	$2$	$2$	$1.078$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$1$	$0$	$-2$	$2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+(2-2\beta )q^{7}+\cdots$

$ S_{2}^{\mathrm{old}}(\Gamma_0(135)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(15))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(27))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(45))$$^{\oplus 2}$

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\(3\)	\(5\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(+\)	$-$	\(2\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(5\)