LMFDB - Space of modular forms of level 27, weight 4, and trivial character

Defining parameters

The following table gives the dimensions of various subspaces of $M_{4}(\Gamma_0(27))$.

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

$3$	Total			Cusp			Eisenstein
$3$	All	New	Old	All	New	Old	All	New	Old
$+$	$7$	$3$	$4$	$4$	$3$	$1$	$3$	$0$	$3$
$-$	$5$	$1$	$4$	$2$	$1$	$1$	$3$	$0$	$3$

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
27.4.a.a	$27$	$4$	27.a	1.a	$1$	$1$	$1$	$1.593$	$\Q$	None	✓	✓	✓	✓	27.4.a.a	$1$	$1$	$-3$	$0$	$-15$	$-25$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}+q^{4}-15q^{5}-5^{2}q^{7}+21q^{8}+\cdots$
27.4.a.b	$27$	$4$	27.a	1.a	$1$	$1$	$1$	$1.593$	$\Q$	None	✓	✓			27.4.a.a	$1$	$0$	$3$	$0$	$15$	$-25$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}+q^{4}+15q^{5}-5^{2}q^{7}-21q^{8}+\cdots$
27.4.a.c	$27$	$4$	27.a	1.a	$1$	$2$	$2$	$1.593$	$\Q(\sqrt{2}) $	None	✓	✓	✓		27.4.a.c	$2$	$0$	$0$	$0$	$0$	$22$	$+$	$+$	$3$	$\mathrm{SU}(2)$	$q+\beta q^{2}+10q^{4}-4\beta q^{5}+11q^{7}+2\beta q^{8}+\cdots$

$ S_{4}^{\mathrm{old}}(\Gamma_0(27)) \simeq $ $S_{4}^{\mathrm{new}}(\Gamma_0(9))$$^{\oplus 2}$

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\(3\)	Total			Cusp			Eisenstein
\(3\)	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(7\)	\(3\)	\(4\)	\(4\)	\(3\)	\(1\)	\(3\)	\(0\)	\(3\)
\(-\)	\(5\)	\(1\)	\(4\)	\(2\)	\(1\)	\(1\)	\(3\)	\(0\)	\(3\)