Space of modular forms of level 2169, weight 2, and trivial character

• Label: 2169.2.a
• Level: $2169$
• Weight: $2$
• Character orbit: 2169.a
• Rep. character: $\chi_{2169}(1,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $11$
• Sturm bound: $484$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2169 = 3^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2169.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(484\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2169))\).

	Total	New	Old
Modular forms	246	100	146
Cusp forms	239	100	139
Eisenstein series	7	0	7

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
\(+\)	\(+\)	$+$	\(14\)
\(+\)	\(-\)	$-$	\(26\)
\(-\)	\(+\)	$-$	\(33\)
\(-\)	\(-\)	$+$	\(27\)
Plus space		\(+\)	\(41\)
Minus space		\(-\)	\(59\)

Trace form

\( 100 q + 2 q^{2} + 102 q^{4} + 4 q^{7} + 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2169))\) 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
2169.2.a.a	$2169$	$2$	2169.a	1.a	$1$	$1$	$1$	$17.320$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-2q^{7}+q^{11}+4q^{16}+2q^{17}+\cdots\)
2169.2.a.b	$2169$	$2$	2169.a	1.a	$1$	$1$	$1$	$17.320$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots\)
2169.2.a.c	$2169$	$2$	2169.a	1.a	$1$	$2$	$2$	$17.320$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-4\)	\(2\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+(1+\beta )q^{7}+3q^{8}+\cdots\)
2169.2.a.d	$2169$	$2$	2169.a	1.a	$1$	$5$	$5$	$17.320$	5.5.24217.1	None	✓	$1$	$1$	\(2\)	\(0\)	\(8\)	\(-7\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}-\beta _{4}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
2169.2.a.e	$2169$	$2$	2169.a	1.a	$1$	$7$	$7$	$17.320$	7.7.31056073.1	None	✓	$1$	$0$	\(4\)	\(0\)	\(8\)	\(-7\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
2169.2.a.f	$2169$	$2$	2169.a	1.a	$1$	$9$	$9$	$17.320$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-12\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{8})q^{5}+\cdots\)
2169.2.a.g	$2169$	$2$	2169.a	1.a	$1$	$10$	$10$	$17.320$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(10\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{9}q^{2}+(1+\beta _{7}-\beta _{9})q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
2169.2.a.h	$2169$	$2$	2169.a	1.a	$1$	$12$	$12$	$17.320$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-6\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{9})q^{5}+\cdots\)
2169.2.a.i	$2169$	$2$	2169.a	1.a	$1$	$13$	$13$	$17.320$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-6\)	\(9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{7}q^{5}+(1+\beta _{11}+\cdots)q^{7}+\cdots\)
2169.2.a.j	$2169$	$2$	2169.a	1.a	$1$	$14$	$14$	$17.320$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-14\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{12}q^{5}+(-1-\beta _{8}+\cdots)q^{7}+\cdots\)
2169.2.a.k	$2169$	$2$	2169.a	1.a	$1$	$26$	$26$	$17.320$		None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(22\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2169))\) into lower level spaces

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