Space of modular forms of level 8032, weight 2, and trivial character

• Label: 8032.2.a
• Level: $8032$
• Weight: $2$
• Character orbit: 8032.a
• Rep. character: $\chi_{8032}(1,\cdot)$
• Character field: $\Q$
• Dimension: $250$
• Newform subspaces: $12$
• Sturm bound: $2016$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 8032 = 2^{5} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8032.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(2016\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8032))\).

	Total	New	Old
Modular forms	1016	250	766
Cusp forms	1001	250	751
Eisenstein series	15	0	15

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

\(2\)	\(251\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(59\)
\(+\)	\(-\)	$-$	\(66\)
\(-\)	\(+\)	$-$	\(66\)
\(-\)	\(-\)	$+$	\(59\)
Plus space		\(+\)	\(118\)
Minus space		\(-\)	\(132\)

Trace form

\( 250 q + 4 q^{5} + 250 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8032))\) 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	251
8032.2.a.a	$8032$	$2$	8032.a	1.a	$1$	$1$	$1$	$64.136$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{7}-3q^{9}-6q^{11}-6q^{13}+\cdots\)
8032.2.a.b	$8032$	$2$	8032.a	1.a	$1$	$1$	$1$	$64.136$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{7}-3q^{9}+2q^{11}+2q^{13}+\cdots\)
8032.2.a.c	$8032$	$2$	8032.a	1.a	$1$	$1$	$1$	$64.136$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}-3q^{9}-2q^{11}+2q^{13}+\cdots\)
8032.2.a.d	$8032$	$2$	8032.a	1.a	$1$	$1$	$1$	$64.136$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}-3q^{9}+6q^{11}-6q^{13}+\cdots\)
8032.2.a.e	$8032$	$2$	8032.a	1.a	$1$	$28$	$28$	$64.136$		None	✓	$1$	$1$	\(0\)	\(-3\)	\(-13\)	\(7\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
8032.2.a.f	$8032$	$2$	8032.a	1.a	$1$	$28$	$28$	$64.136$		None	✓	$1$	$1$	\(0\)	\(3\)	\(-13\)	\(-7\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8032.2.a.g	$8032$	$2$	8032.a	1.a	$1$	$30$	$30$	$64.136$		None	✓	$1$	$1$	\(0\)	\(-9\)	\(0\)	\(-5\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8032.2.a.h	$8032$	$2$	8032.a	1.a	$1$	$30$	$30$	$64.136$		None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-13\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
8032.2.a.i	$8032$	$2$	8032.a	1.a	$1$	$30$	$30$	$64.136$		None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(13\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
8032.2.a.j	$8032$	$2$	8032.a	1.a	$1$	$30$	$30$	$64.136$		None	✓	$1$	$0$	\(0\)	\(9\)	\(0\)	\(5\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
8032.2.a.k	$8032$	$2$	8032.a	1.a	$1$	$35$	$35$	$64.136$		None	✓	$1$	$0$	\(0\)	\(-3\)	\(13\)	\(7\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
8032.2.a.l	$8032$	$2$	8032.a	1.a	$1$	$35$	$35$	$64.136$		None	✓	$1$	$0$	\(0\)	\(3\)	\(13\)	\(-7\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8032))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8032)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(251))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(502))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1004))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2008))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4016))\)\(^{\oplus 2}\)