Space of modular forms of level 6041, weight 2, and trivial character

• Label: 6041.2.a
• Level: $6041$
• Weight: $2$
• Character orbit: 6041.a
• Rep. character: $\chi_{6041}(1,\cdot)$
• Character field: $\Q$
• Dimension: $431$
• Newform subspaces: $6$
• Sturm bound: $1152$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1152\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6041))\).

	Total	New	Old
Modular forms	578	431	147
Cusp forms	575	431	144
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.

\(7\)	\(863\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(103\)
\(+\)	\(-\)	$-$	\(112\)
\(-\)	\(+\)	$-$	\(133\)
\(-\)	\(-\)	$+$	\(83\)
Plus space		\(+\)	\(186\)
Minus space		\(-\)	\(245\)

Trace form

\( 431 q - q^{2} + 435 q^{4} - 2 q^{5} + 8 q^{6} + q^{7} + 3 q^{8} + 423 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6041))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	863
6041.2.a.a	$6041$	$2$	6041.a	1.a	$1$	$1$	$1$	$48.238$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(2\)	\(-4\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}-q^{4}-4q^{5}+2q^{6}+q^{7}+\cdots\)
6041.2.a.b	$6041$	$2$	6041.a	1.a	$1$	$2$	$2$	$48.238$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-2\)	\(3\)	\(1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}-q^{4}+(1-\beta )q^{5}+\cdots\)
6041.2.a.c	$6041$	$2$	6041.a	1.a	$1$	$83$	$83$	$48.238$		None	✓	$1$	$1$	\(-8\)	\(-12\)	\(-11\)	\(83\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6041.2.a.d	$6041$	$2$	6041.a	1.a	$1$	$101$	$101$	$48.238$		None	✓	$1$	$1$	\(3\)	\(-17\)	\(-12\)	\(-101\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6041.2.a.e	$6041$	$2$	6041.a	1.a	$1$	$112$	$112$	$48.238$		None	✓	$1$	$0$	\(-3\)	\(14\)	\(13\)	\(-112\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6041.2.a.f	$6041$	$2$	6041.a	1.a	$1$	$132$	$132$	$48.238$		None	✓	$1$	$0$	\(8\)	\(10\)	\(11\)	\(132\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6041))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6041)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(863))\)\(^{\oplus 2}\)