Space of modular forms of level 6022, weight 2, and trivial character

• Label: 6022.2.a
• Level: $6022$
• Weight: $2$
• Character orbit: 6022.a
• Rep. character: $\chi_{6022}(1,\cdot)$
• Character field: $\Q$
• Dimension: $250$
• Newform subspaces: $5$
• Sturm bound: $1506$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1506\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6022))\).

	Total	New	Old
Modular forms	755	250	505
Cusp forms	752	250	502
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.

\(2\)	\(3011\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(64\)
\(+\)	\(-\)	$-$	\(61\)
\(-\)	\(+\)	$-$	\(71\)
\(-\)	\(-\)	$+$	\(54\)
Plus space		\(+\)	\(118\)
Minus space		\(-\)	\(132\)

Trace form

\( 250 q - 2 q^{3} + 250 q^{4} - 2 q^{5} + 248 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6022))\) 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	3011
6022.2.a.a	$6022$	$2$	6022.a	1.a	$1$	$3$	$3$	$48.086$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$2$	\(3\)	\(-4\)	\(-7\)	\(-9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-3+\beta _{1}+\cdots)q^{5}+\cdots\)
6022.2.a.b	$6022$	$2$	6022.a	1.a	$1$	$54$	$54$	$48.086$		None	✓	$1$	$1$	\(54\)	\(-22\)	\(-14\)	\(-20\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6022.2.a.c	$6022$	$2$	6022.a	1.a	$1$	$61$	$61$	$48.086$		None	✓	$1$	$0$	\(-61\)	\(8\)	\(16\)	\(2\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6022.2.a.d	$6022$	$2$	6022.a	1.a	$1$	$64$	$64$	$48.086$		None	✓	$1$	$1$	\(-64\)	\(-9\)	\(-17\)	\(-2\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6022.2.a.e	$6022$	$2$	6022.a	1.a	$1$	$68$	$68$	$48.086$		None	✓	$1$	$0$	\(68\)	\(25\)	\(20\)	\(29\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6022))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6022)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(3011))\)\(^{\oplus 2}\)