Space of modular forms of level 2169, weight 4, and trivial character

• Label: 2169.4.a
• Level: $2169$
• Weight: $4$
• Character orbit: 2169.a
• Rep. character: $\chi_{2169}(1,\cdot)$
• Character field: $\Q$
• Dimension: $300$
• Newform subspaces: $8$
• Sturm bound: $968$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2169 = 3^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2169.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(968\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2169))\).

	Total	New	Old
Modular forms	730	300	430
Cusp forms	722	300	422
Eisenstein series	8	0	8

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

\(3\)	\(241\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(66\)
\(+\)	\(-\)	$-$	\(54\)
\(-\)	\(+\)	$-$	\(87\)
\(-\)	\(-\)	$+$	\(93\)
Plus space		\(+\)	\(159\)
Minus space		\(-\)	\(141\)

Trace form

\( 300 q - 2 q^{2} + 1210 q^{4} - 16 q^{5} - 10 q^{7} - 30 q^{8} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2169))\) 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	241
2169.4.a.a	$2169$	$4$	2169.a	1.a	$1$	$25$	$25$	$127.975$		None	✓	$1$	$1$	\(7\)	\(0\)	\(54\)	\(-86\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2169.4.a.b	$2169$	$4$	2169.a	1.a	$1$	$27$	$27$	$127.975$		None	✓	$1$	$0$	\(11\)	\(0\)	\(50\)	\(-68\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2169.4.a.c	$2169$	$4$	2169.a	1.a	$1$	$29$	$29$	$127.975$		None	✓	$1$	$1$	\(-9\)	\(0\)	\(-62\)	\(-30\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2169.4.a.d	$2169$	$4$	2169.a	1.a	$1$	$31$	$31$	$127.975$		None	✓	$1$	$0$	\(7\)	\(0\)	\(58\)	\(26\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2169.4.a.e	$2169$	$4$	2169.a	1.a	$1$	$33$	$33$	$127.975$		None	✓	$1$	$1$	\(-9\)	\(0\)	\(-50\)	\(58\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2169.4.a.f	$2169$	$4$	2169.a	1.a	$1$	$35$	$35$	$127.975$		None	✓	$1$	$0$	\(-9\)	\(0\)	\(-66\)	\(110\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2169.4.a.g	$2169$	$4$	2169.a	1.a	$1$	$54$	$54$	$127.975$		None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-136\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
2169.4.a.h	$2169$	$4$	2169.a	1.a	$1$	$66$	$66$	$127.975$		None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(116\)		$+$	$+$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2169))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2169)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(241))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(723))\)\(^{\oplus 2}\)