Space of modular forms of level 8043, weight 2, and trivial character

• Label: 8043.2.a
• Level: $8043$
• Weight: $2$
• Character orbit: 8043.a
• Rep. character: $\chi_{8043}(1,\cdot)$
• Character field: $\Q$
• Dimension: $383$
• Newform subspaces: $21$
• Sturm bound: $2048$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 21 \)
Sturm bound:			\(2048\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8043))\).

	Total	New	Old
Modular forms	1028	383	645
Cusp forms	1021	383	638
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.

\(3\)	\(7\)	\(383\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(46\)
\(+\)	\(+\)	\(-\)	$-$	\(50\)
\(+\)	\(-\)	\(+\)	$-$	\(54\)
\(+\)	\(-\)	\(-\)	$+$	\(42\)
\(-\)	\(+\)	\(+\)	$-$	\(49\)
\(-\)	\(+\)	\(-\)	$+$	\(45\)
\(-\)	\(-\)	\(+\)	$+$	\(43\)
\(-\)	\(-\)	\(-\)	$-$	\(54\)
Plus space			\(+\)	\(176\)
Minus space			\(-\)	\(207\)

Trace form

\( 383 q + 5 q^{2} - q^{3} + 385 q^{4} + 10 q^{5} - 3 q^{6} + 3 q^{7} + 9 q^{8} + 383 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8043))\) 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	7	383
8043.2.a.a	$8043$	$2$	8043.a	1.a	$1$	$1$	$1$	$64.224$	\(\Q\)	None	✓	$1$	$2$	\(-2\)	\(1\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots\)
8043.2.a.b	$8043$	$2$	8043.a	1.a	$1$	$1$	$1$	$64.224$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
8043.2.a.c	$8043$	$2$	8043.a	1.a	$1$	$1$	$1$	$64.224$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
8043.2.a.d	$8043$	$2$	8043.a	1.a	$1$	$1$	$1$	$64.224$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
8043.2.a.e	$8043$	$2$	8043.a	1.a	$1$	$1$	$1$	$64.224$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-5q^{11}+\cdots\)
8043.2.a.f	$8043$	$2$	8043.a	1.a	$1$	$1$	$1$	$64.224$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}-3q^{11}+\cdots\)
8043.2.a.g	$8043$	$2$	8043.a	1.a	$1$	$1$	$1$	$64.224$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+2q^{5}-q^{7}+q^{9}+3q^{11}+\cdots\)
8043.2.a.h	$8043$	$2$	8043.a	1.a	$1$	$1$	$1$	$64.224$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots\)
8043.2.a.i	$8043$	$2$	8043.a	1.a	$1$	$1$	$1$	$64.224$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(-1\)	\(3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots\)
8043.2.a.j	$8043$	$2$	8043.a	1.a	$1$	$1$	$1$	$64.224$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(-1\)	\(3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots\)
8043.2.a.k	$8043$	$2$	8043.a	1.a	$1$	$1$	$1$	$64.224$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(1\)	\(1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
8043.2.a.l	$8043$	$2$	8043.a	1.a	$1$	$2$	$2$	$64.224$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(-1\)	\(2\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
8043.2.a.m	$8043$	$2$	8043.a	1.a	$1$	$3$	$3$	$64.224$	3.3.148.1	None	✓	$1$	$0$	\(-1\)	\(3\)	\(-2\)	\(-3\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
8043.2.a.n	$8043$	$2$	8043.a	1.a	$1$	$40$	$40$	$64.224$		None	✓	$1$	$1$	\(-9\)	\(40\)	\(-27\)	\(40\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
8043.2.a.o	$8043$	$2$	8043.a	1.a	$1$	$41$	$41$	$64.224$		None	✓	$1$	$1$	\(-4\)	\(-41\)	\(5\)	\(41\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8043.2.a.p	$8043$	$2$	8043.a	1.a	$1$	$41$	$41$	$64.224$		None	✓	$1$	$0$	\(7\)	\(41\)	\(17\)	\(-41\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
8043.2.a.q	$8043$	$2$	8043.a	1.a	$1$	$44$	$44$	$64.224$		None	✓	$1$	$1$	\(-4\)	\(44\)	\(-16\)	\(-44\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
8043.2.a.r	$8043$	$2$	8043.a	1.a	$1$	$46$	$46$	$64.224$		None	✓	$1$	$1$	\(3\)	\(-46\)	\(-9\)	\(-46\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8043.2.a.s	$8043$	$2$	8043.a	1.a	$1$	$50$	$50$	$64.224$		None	✓	$1$	$0$	\(-1\)	\(-50\)	\(11\)	\(-50\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8043.2.a.t	$8043$	$2$	8043.a	1.a	$1$	$52$	$52$	$64.224$		None	✓	$1$	$0$	\(3\)	\(-52\)	\(-7\)	\(52\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
8043.2.a.u	$8043$	$2$	8043.a	1.a	$1$	$53$	$53$	$64.224$		None	✓	$1$	$0$	\(11\)	\(53\)	\(24\)	\(53\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8043))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8043)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(383))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1149))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2681))\)\(^{\oplus 2}\)