Space of modular forms of level 4023, weight 2, and trivial character

• Label: 4023.2.a
• Level: $4023$
• Weight: $2$
• Character orbit: 4023.a
• Rep. character: $\chi_{4023}(1,\cdot)$
• Character field: $\Q$
• Dimension: $198$
• Newform subspaces: $8$
• Sturm bound: $900$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 4023 = 3^{3} \cdot 149 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4023.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(900\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4023))\).

	Total	New	Old
Modular forms	456	198	258
Cusp forms	445	198	247
Eisenstein series	11	0	11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(149\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(43\)
\(+\)	\(-\)	$-$	\(57\)
\(-\)	\(+\)	$-$	\(56\)
\(-\)	\(-\)	$+$	\(42\)
Plus space		\(+\)	\(85\)
Minus space		\(-\)	\(113\)

Trace form

\( 198 q + 204 q^{4} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4023))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	149
4023.2.a.a	$4023$	$2$	4023.a	1.a	$1$	$18$	$18$	$32.124$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-11\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{17}q^{5}+(-1+\cdots)q^{7}+\cdots\)
4023.2.a.b	$4023$	$2$	4023.a	1.a	$1$	$18$	$18$	$32.124$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-11\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{17}q^{5}+(-1+\cdots)q^{7}+\cdots\)
4023.2.a.c	$4023$	$2$	4023.a	1.a	$1$	$24$	$24$	$32.124$		None	✓	$1$	$1$	\(-7\)	\(0\)	\(-12\)	\(-1\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
4023.2.a.d	$4023$	$2$	4023.a	1.a	$1$	$24$	$24$	$32.124$		None	✓	$1$	$0$	\(7\)	\(0\)	\(12\)	\(-1\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
4023.2.a.e	$4023$	$2$	4023.a	1.a	$1$	$25$	$25$	$32.124$		None	✓	$1$	$1$	\(-7\)	\(0\)	\(-12\)	\(-2\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
4023.2.a.f	$4023$	$2$	4023.a	1.a	$1$	$25$	$25$	$32.124$		None	✓	$1$	$0$	\(7\)	\(0\)	\(12\)	\(-2\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
4023.2.a.g	$4023$	$2$	4023.a	1.a	$1$	$32$	$32$	$32.124$		None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(13\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
4023.2.a.h	$4023$	$2$	4023.a	1.a	$1$	$32$	$32$	$32.124$		None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(13\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4023))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4023)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(149))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(447))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1341))\)\(^{\oplus 2}\)