Space of modular forms of level 8033, weight 2, and trivial character

• Label: 8033.2.a
• Level: $8033$
• Weight: $2$
• Character orbit: 8033.a
• Rep. character: $\chi_{8033}(1,\cdot)$
• Character field: $\Q$
• Dimension: $645$
• Newform subspaces: $5$
• Sturm bound: $1390$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1390\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8033))\).

	Total	New	Old
Modular forms	696	645	51
Cusp forms	693	645	48
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.

\(29\)	\(277\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(153\)
\(+\)	\(-\)	$-$	\(169\)
\(-\)	\(+\)	$-$	\(169\)
\(-\)	\(-\)	$+$	\(154\)
Plus space		\(+\)	\(307\)
Minus space		\(-\)	\(338\)

Trace form

\( 645 q + q^{2} - 4 q^{3} + 643 q^{4} + 2 q^{5} + 8 q^{7} - 3 q^{8} + 641 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8033))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		29	277
8033.2.a.a	$8033$	$2$	8033.a	1.a	$1$	$1$	$1$	$64.144$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(-3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}-3q^{5}+q^{6}+2q^{7}+\cdots\)
8033.2.a.b	$8033$	$2$	8033.a	1.a	$1$	$153$	$153$	$64.144$		None	✓	$1$	$1$	\(-3\)	\(-12\)	\(-11\)	\(-76\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
8033.2.a.c	$8033$	$2$	8033.a	1.a	$1$	$154$	$154$	$64.144$		None	✓	$1$	$1$	\(-12\)	\(-36\)	\(-9\)	\(-68\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8033.2.a.d	$8033$	$2$	8033.a	1.a	$1$	$168$	$168$	$64.144$		None	✓	$1$	$0$	\(12\)	\(35\)	\(12\)	\(74\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
8033.2.a.e	$8033$	$2$	8033.a	1.a	$1$	$169$	$169$	$64.144$		None	✓	$1$	$0$	\(3\)	\(8\)	\(13\)	\(76\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8033))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8033)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(277))\)\(^{\oplus 2}\)