Space of modular forms of level 8002, weight 2, and trivial character

• Label: 8002.2.a
• Level: $8002$
• Weight: $2$
• Character orbit: 8002.a
• Rep. character: $\chi_{8002}(1,\cdot)$
• Character field: $\Q$
• Dimension: $333$
• Newform subspaces: $7$
• Sturm bound: $2001$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(2001\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8002))\).

	Total	New	Old
Modular forms	1002	333	669
Cusp forms	999	333	666
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.

\(2\)	\(4001\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(89\)
\(+\)	\(-\)	$-$	\(77\)
\(-\)	\(+\)	$-$	\(95\)
\(-\)	\(-\)	$+$	\(72\)
Plus space		\(+\)	\(161\)
Minus space		\(-\)	\(172\)

Trace form

\( 333 q + q^{2} - 2 q^{3} + 333 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + q^{8} + 337 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8002))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	4001
8002.2.a.a	$8002$	$2$	8002.a	1.a	$1$	$1$	$1$	$63.896$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
8002.2.a.b	$8002$	$2$	8002.a	1.a	$1$	$1$	$1$	$63.896$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+4q^{13}+\cdots\)
8002.2.a.c	$8002$	$2$	8002.a	1.a	$1$	$1$	$1$	$63.896$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+q^{8}+\cdots\)
8002.2.a.d	$8002$	$2$	8002.a	1.a	$1$	$69$	$69$	$63.896$		None	✓	$1$	$1$	\(69\)	\(-25\)	\(-33\)	\(-19\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8002.2.a.e	$8002$	$2$	8002.a	1.a	$1$	$77$	$77$	$63.896$		None	✓	$1$	$0$	\(-77\)	\(10\)	\(18\)	\(21\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
8002.2.a.f	$8002$	$2$	8002.a	1.a	$1$	$89$	$89$	$63.896$		None	✓	$1$	$1$	\(-89\)	\(-12\)	\(-18\)	\(-27\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
8002.2.a.g	$8002$	$2$	8002.a	1.a	$1$	$95$	$95$	$63.896$		None	✓	$1$	$0$	\(95\)	\(24\)	\(36\)	\(21\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4001))\)\(^{\oplus 2}\)