Space of modular forms of level 8017, weight 2, and trivial character

• Label: 8017.2.a
• Level: $8017$
• Weight: $2$
• Character orbit: 8017.a
• Rep. character: $\chi_{8017}(1,\cdot)$
• Character field: $\Q$
• Dimension: $667$
• Newform subspaces: $2$
• Sturm bound: $1336$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1336\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8017))\).

	Total	New	Old
Modular forms	668	668	0
Cusp forms	667	667	0
Eisenstein series	1	1	0

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

\(8017\)	Dim
\(+\)	\(327\)
\(-\)	\(340\)

Trace form

\( 667 q - 3 q^{2} - 4 q^{3} + 665 q^{4} - 2 q^{5} - 4 q^{6} - 6 q^{7} - 15 q^{8} + 663 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8017))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		8017
8017.2.a.a	$8017$	$2$	8017.a	1.a	$1$	$327$	$327$	$64.016$		None	✓	$1$	$1$	\(-23\)	\(-48\)	\(-55\)	\(-87\)		$+$	$+$		$\mathrm{SU}(2)$
8017.2.a.b	$8017$	$2$	8017.a	1.a	$1$	$340$	$340$	$64.016$		None	✓	$1$	$0$	\(20\)	\(44\)	\(53\)	\(81\)		$-$	$-$		$\mathrm{SU}(2)$