Space of modular forms of level 8007, weight 2, and trivial character

• Label: 8007.2.a
• Level: $8007$
• Weight: $2$
• Character orbit: 8007.a
• Rep. character: $\chi_{8007}(1,\cdot)$
• Character field: $\Q$
• Dimension: $415$
• Newform subspaces: $10$
• Sturm bound: $1896$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1896\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8007))\).

	Total	New	Old
Modular forms	952	415	537
Cusp forms	945	415	530
Eisenstein series	7	0	7

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

\(3\)	\(17\)	\(157\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(48\)
\(+\)	\(+\)	\(-\)	$-$	\(56\)
\(+\)	\(-\)	\(+\)	$-$	\(64\)
\(+\)	\(-\)	\(-\)	$+$	\(40\)
\(-\)	\(+\)	\(+\)	$-$	\(56\)
\(-\)	\(+\)	\(-\)	$+$	\(48\)
\(-\)	\(-\)	\(+\)	$+$	\(40\)
\(-\)	\(-\)	\(-\)	$-$	\(63\)
Plus space			\(+\)	\(176\)
Minus space			\(-\)	\(239\)

Trace form

\( 415 q + 5 q^{2} - q^{3} + 417 q^{4} - 6 q^{5} + q^{6} + 8 q^{7} + 9 q^{8} + 415 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8007))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	17	157
8007.2.a.a	$8007$	$2$	8007.a	1.a	$1$	$1$	$1$	$63.936$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{6}+2q^{7}-3q^{8}+\cdots\)
8007.2.a.b	$8007$	$2$	8007.a	1.a	$1$	$2$	$2$	$63.936$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(2\)	\(-4\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
8007.2.a.c	$8007$	$2$	8007.a	1.a	$1$	$39$	$39$	$63.936$		None	✓	$1$	$1$	\(-4\)	\(-39\)	\(-3\)	\(-5\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8007.2.a.d	$8007$	$2$	8007.a	1.a	$1$	$40$	$40$	$63.936$		None	✓	$1$	$1$	\(-7\)	\(40\)	\(-15\)	\(-13\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
8007.2.a.e	$8007$	$2$	8007.a	1.a	$1$	$46$	$46$	$63.936$		None	✓	$1$	$1$	\(-5\)	\(46\)	\(-19\)	\(1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
8007.2.a.f	$8007$	$2$	8007.a	1.a	$1$	$48$	$48$	$63.936$		None	✓	$1$	$1$	\(-1\)	\(-48\)	\(1\)	\(-13\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8007.2.a.g	$8007$	$2$	8007.a	1.a	$1$	$56$	$56$	$63.936$		None	✓	$1$	$0$	\(1\)	\(-56\)	\(1\)	\(19\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8007.2.a.h	$8007$	$2$	8007.a	1.a	$1$	$56$	$56$	$63.936$		None	✓	$1$	$0$	\(7\)	\(56\)	\(17\)	\(5\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
8007.2.a.i	$8007$	$2$	8007.a	1.a	$1$	$63$	$63$	$63.936$		None	✓	$1$	$0$	\(10\)	\(63\)	\(19\)	\(11\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
8007.2.a.j	$8007$	$2$	8007.a	1.a	$1$	$64$	$64$	$63.936$		None	✓	$1$	$0$	\(5\)	\(-64\)	\(-3\)	\(5\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8007))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8007)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(157))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(471))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2669))\)\(^{\oplus 2}\)