Space of modular forms of level 8023, weight 2, and trivial character

• Label: 8023.2.a
• Level: $8023$
• Weight: $2$
• Character orbit: 8023.a
• Rep. character: $\chi_{8023}(1,\cdot)$
• Character field: $\Q$
• Dimension: $653$
• Newform subspaces: $5$
• Sturm bound: $1368$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1368\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8023))\).

	Total	New	Old
Modular forms	686	653	33
Cusp forms	683	653	30
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.

\(71\)	\(113\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(161\)
\(+\)	\(-\)	$-$	\(172\)
\(-\)	\(+\)	$-$	\(165\)
\(-\)	\(-\)	$+$	\(155\)
Plus space		\(+\)	\(316\)
Minus space		\(-\)	\(337\)

Trace form

\( 653 q + 3 q^{2} + 655 q^{4} - 2 q^{5} - 16 q^{7} + 15 q^{8} + 653 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		71	113
8023.2.a.a	$8023$	$2$	8023.a	1.a	$1$	$3$	$3$	$64.064$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(2\)	\(3\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2\beta _{1}-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
8023.2.a.b	$8023$	$2$	8023.a	1.a	$1$	$155$	$155$	$64.064$		None	✓	$1$	$1$	\(-21\)	\(-16\)	\(-26\)	\(-40\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8023.2.a.c	$8023$	$2$	8023.a	1.a	$1$	$158$	$158$	$64.064$		None	✓	$1$	$1$	\(-24\)	\(-23\)	\(-31\)	\(-2\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
8023.2.a.d	$8023$	$2$	8023.a	1.a	$1$	$165$	$165$	$64.064$		None	✓	$1$	$0$	\(22\)	\(18\)	\(28\)	\(24\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
8023.2.a.e	$8023$	$2$	8023.a	1.a	$1$	$172$	$172$	$64.064$		None	✓	$1$	$0$	\(24\)	\(18\)	\(28\)	\(4\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8023))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8023)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(71))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(113))\)\(^{\oplus 2}\)