Space of modular forms of level 6023, weight 2, and trivial character

• Label: 6023.2.a
• Level: $6023$
• Weight: $2$
• Character orbit: 6023.a
• Rep. character: $\chi_{6023}(1,\cdot)$
• Character field: $\Q$
• Dimension: $475$
• Newform subspaces: $4$
• Sturm bound: $1060$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1060\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6023))\).

	Total	New	Old
Modular forms	532	475	57
Cusp forms	529	475	54
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.

\(19\)	\(317\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(99\)
\(+\)	\(-\)	$-$	\(140\)
\(-\)	\(+\)	$-$	\(138\)
\(-\)	\(-\)	$+$	\(98\)
Plus space		\(+\)	\(197\)
Minus space		\(-\)	\(278\)

Trace form

\( 475 q + 3 q^{2} + 4 q^{3} + 481 q^{4} + 4 q^{6} + 6 q^{7} + 15 q^{8} + 471 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6023))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		19	317
6023.2.a.a	$6023$	$2$	6023.a	1.a	$1$	$98$	$98$	$48.094$		None	✓	$1$	$1$	\(-8\)	\(-25\)	\(-10\)	\(-18\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6023.2.a.b	$6023$	$2$	6023.a	1.a	$1$	$99$	$99$	$48.094$		None	✓	$1$	$1$	\(-4\)	\(-3\)	\(-15\)	\(-19\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6023.2.a.c	$6023$	$2$	6023.a	1.a	$1$	$138$	$138$	$48.094$		None	✓	$1$	$0$	\(11\)	\(29\)	\(12\)	\(18\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
6023.2.a.d	$6023$	$2$	6023.a	1.a	$1$	$140$	$140$	$48.094$		None	✓	$1$	$0$	\(4\)	\(3\)	\(13\)	\(25\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6023))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6023)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(317))\)\(^{\oplus 2}\)