Space of modular forms of level 8041, weight 2, and trivial character

• Label: 8041.2.a
• Level: $8041$
• Weight: $2$
• Character orbit: 8041.a
• Rep. character: $\chi_{8041}(1,\cdot)$
• Character field: $\Q$
• Dimension: $559$
• Newform subspaces: $10$
• Sturm bound: $1584$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1584\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8041))\).

	Total	New	Old
Modular forms	796	559	237
Cusp forms	789	559	230
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.

\(11\)	\(17\)	\(43\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(74\)
\(+\)	\(+\)	\(-\)	$-$	\(66\)
\(+\)	\(-\)	\(+\)	$-$	\(67\)
\(+\)	\(-\)	\(-\)	$+$	\(69\)
\(-\)	\(+\)	\(+\)	$-$	\(78\)
\(-\)	\(+\)	\(-\)	$+$	\(62\)
\(-\)	\(-\)	\(+\)	$+$	\(61\)
\(-\)	\(-\)	\(-\)	$-$	\(82\)
Plus space			\(+\)	\(266\)
Minus space			\(-\)	\(293\)

Trace form

\( 559 q - 3 q^{2} + 553 q^{4} - 2 q^{5} + 12 q^{6} - 8 q^{7} + 33 q^{8} + 551 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8041))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11	17	43
8041.2.a.a	$8041$	$2$	8041.a	1.a	$1$	$1$	$1$	$64.208$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-2\)	\(2\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+2q^{4}+2q^{5}+4q^{6}+\cdots\)
8041.2.a.b	$8041$	$2$	8041.a	1.a	$1$	$1$	$1$	$64.208$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(3\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-q^{4}-2q^{5}-3q^{6}-2q^{7}+\cdots\)
8041.2.a.c	$8041$	$2$	8041.a	1.a	$1$	$60$	$60$	$64.208$		None	✓	$1$	$1$	\(-9\)	\(-6\)	\(-15\)	\(-17\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
8041.2.a.d	$8041$	$2$	8041.a	1.a	$1$	$62$	$62$	$64.208$		None	✓	$1$	$1$	\(-7\)	\(-8\)	\(-13\)	\(-11\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
8041.2.a.e	$8041$	$2$	8041.a	1.a	$1$	$66$	$66$	$64.208$		None	✓	$1$	$0$	\(7\)	\(3\)	\(4\)	\(14\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8041.2.a.f	$8041$	$2$	8041.a	1.a	$1$	$66$	$66$	$64.208$		None	✓	$1$	$0$	\(12\)	\(0\)	\(6\)	\(13\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
8041.2.a.g	$8041$	$2$	8041.a	1.a	$1$	$69$	$69$	$64.208$		None	✓	$1$	$1$	\(-11\)	\(-3\)	\(-6\)	\(-11\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8041.2.a.h	$8041$	$2$	8041.a	1.a	$1$	$74$	$74$	$64.208$		None	✓	$1$	$1$	\(-7\)	\(-3\)	\(-6\)	\(-16\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8041.2.a.i	$8041$	$2$	8041.a	1.a	$1$	$78$	$78$	$64.208$		None	✓	$1$	$0$	\(7\)	\(10\)	\(17\)	\(11\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
8041.2.a.j	$8041$	$2$	8041.a	1.a	$1$	$82$	$82$	$64.208$		None	✓	$1$	$0$	\(8\)	\(6\)	\(11\)	\(8\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8041))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8041)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(473))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(731))\)\(^{\oplus 2}\)