LMFDB - Space of modular forms of level 3004, weight 2, and trivial character

Defining parameters

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(3004))$.

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

$2$	$751$	Fricke	Dim
$-$	$+$	$-$	$31$
$-$	$-$	$+$	$31$
Plus space		$+$	$31$
Minus space		$-$	$31$

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	751	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3004.2.a.a	$3004$	$2$	3004.a	1.a	$1$	$1$	$1$	$23.987$	$\Q$	None	✓	$1$	$2$	$0$	$-2$	$-2$	$-2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots$
3004.2.a.b	$3004$	$2$	3004.a	1.a	$1$	$2$	$2$	$23.987$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(3-\beta )q^{7}+(1+2\beta )q^{9}+\cdots$
3004.2.a.c	$3004$	$2$	3004.a	1.a	$1$	$28$	$28$	$23.987$		None	✓	$1$	$0$	$0$	$8$	$11$	$5$	$-$	$+$	$-$		$\mathrm{SU}(2)$
3004.2.a.d	$3004$	$2$	3004.a	1.a	$1$	$31$	$31$	$23.987$		None	✓	$1$	$1$	$0$	$-10$	$-11$	$-7$	$-$	$-$	$+$		$\mathrm{SU}(2)$

$ S_{2}^{\mathrm{old}}(\Gamma_0(3004)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(751))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(1502))$$^{\oplus 2}$

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\(2\)	\(751\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(31\)
\(-\)	\(-\)	$+$	\(31\)
Plus space		\(+\)	\(31\)
Minus space		\(-\)	\(31\)