Space of modular forms of level 8047, weight 2, and trivial character

• Label: 8047.2.a
• Level: $8047$
• Weight: $2$
• Character orbit: 8047.a
• Rep. character: $\chi_{8047}(1,\cdot)$
• Character field: $\Q$
• Dimension: $619$
• Newform subspaces: $5$
• Sturm bound: $1446$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 8047 = 13 \cdot 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8047.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1446\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8047))\).

	Total	New	Old
Modular forms	724	619	105
Cusp forms	721	619	102
Eisenstein series	3	0	3

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

\(13\)	\(619\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(151\)
\(+\)	\(-\)	$-$	\(158\)
\(-\)	\(+\)	$-$	\(168\)
\(-\)	\(-\)	$+$	\(142\)
Plus space		\(+\)	\(293\)
Minus space		\(-\)	\(326\)

Trace form

\( 619 q - q^{2} + 4 q^{3} + 621 q^{4} + 2 q^{5} - 4 q^{7} - 9 q^{8} + 623 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8047))\) into newform subspaces

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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		13	619
8047.2.a.a	$8047$	$2$	8047.a	1.a	$1$	$2$	$2$	$64.256$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(1\)	\(-3\)	\(2\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
8047.2.a.b	$8047$	$2$	8047.a	1.a	$1$	$142$	$142$	$64.256$		None	✓	$1$	$1$	\(-13\)	\(-26\)	\(-37\)	\(-14\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8047.2.a.c	$8047$	$2$	8047.a	1.a	$1$	$151$	$151$	$64.256$		None	✓	$1$	$1$	\(-13\)	\(-16\)	\(-43\)	\(-18\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
8047.2.a.d	$8047$	$2$	8047.a	1.a	$1$	$156$	$156$	$64.256$		None	✓	$1$	$0$	\(13\)	\(23\)	\(39\)	\(19\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
8047.2.a.e	$8047$	$2$	8047.a	1.a	$1$	$168$	$168$	$64.256$		None	✓	$1$	$0$	\(11\)	\(26\)	\(41\)	\(12\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8047))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8047)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(619))\)\(^{\oplus 2}\)