Space of modular forms of level 8005, weight 2, and trivial character

• Label: 8005.2.a
• Level: $8005$
• Weight: $2$
• Character orbit: 8005.a
• Rep. character: $\chi_{8005}(1,\cdot)$
• Character field: $\Q$
• Dimension: $533$
• Newform subspaces: $8$
• Sturm bound: $1602$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1602\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8005))\).

	Total	New	Old
Modular forms	802	533	269
Cusp forms	799	533	266
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.

\(5\)	\(1601\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(127\)
\(+\)	\(-\)	$-$	\(139\)
\(-\)	\(+\)	$-$	\(139\)
\(-\)	\(-\)	$+$	\(128\)
Plus space		\(+\)	\(255\)
Minus space		\(-\)	\(278\)

Trace form

\( 533 q - q^{2} + 527 q^{4} + q^{5} - 4 q^{6} - 8 q^{7} - 9 q^{8} + 537 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8005))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	1601
8005.2.a.a	$8005$	$2$	8005.a	1.a	$1$	$1$	$1$	$63.920$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)
8005.2.a.b	$8005$	$2$	8005.a	1.a	$1$	$1$	$1$	$63.920$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(2\)	\(1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}-q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
8005.2.a.c	$8005$	$2$	8005.a	1.a	$1$	$2$	$2$	$63.920$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$2$	\(-1\)	\(-2\)	\(2\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
8005.2.a.d	$8005$	$2$	8005.a	1.a	$1$	$2$	$2$	$63.920$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}-q^{4}-q^{5}+\beta q^{6}-\beta q^{7}+\cdots\)
8005.2.a.e	$8005$	$2$	8005.a	1.a	$1$	$126$	$126$	$63.920$		None	✓	$1$	$1$	\(-15\)	\(-46\)	\(126\)	\(-60\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8005.2.a.f	$8005$	$2$	8005.a	1.a	$1$	$127$	$127$	$63.920$		None	✓	$1$	$1$	\(-6\)	\(-18\)	\(-127\)	\(28\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
8005.2.a.g	$8005$	$2$	8005.a	1.a	$1$	$137$	$137$	$63.920$		None	✓	$1$	$0$	\(4\)	\(20\)	\(-137\)	\(-30\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
8005.2.a.h	$8005$	$2$	8005.a	1.a	$1$	$137$	$137$	$63.920$		None	✓	$1$	$0$	\(17\)	\(46\)	\(137\)	\(53\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1601))\)\(^{\oplus 2}\)