Space of modular forms of level 2169, weight 2, and Character 2169.d

• Label: 2169.2.d
• Level: $2169$
• Weight: $2$
• Character orbit: 2169.d
• Rep. character: $\chi_{2169}(1927,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $6$
• Sturm bound: $484$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 2169 = 3^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2169.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 241 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(484\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2169, [\chi])\).

	Total	New	Old
Modular forms	246	102	144
Cusp forms	238	100	138
Eisenstein series	8	2	6

Trace form

\( 100 q + 2 q^{2} + 102 q^{4} + 4 q^{5} + 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2169, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2169.2.d.a	$2169$	$2$	2169.d	241.b	$2$	$4$	$4$	$17.320$	4.0.696972.1	\(\Q(\sqrt{-723}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{4}+\beta _{2}q^{11}+4q^{16}+\beta _{1}q^{17}+\cdots\)
2169.2.d.b	$2169$	$2$	2169.d	241.b	$2$	$4$	$4$	$17.320$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+q^{4}+(2-\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
2169.2.d.c	$2169$	$2$	2169.d	241.b	$2$	$16$	$16$	$17.320$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{11}q^{2}+(1-\beta _{5}+\beta _{6}-\beta _{8})q^{4}+\cdots\)
2169.2.d.d	$2169$	$2$	2169.d	241.b	$2$	$18$	$18$	$17.320$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{2}q^{4}+\beta _{13}q^{5}+\beta _{1}q^{7}+\cdots\)
2169.2.d.e	$2169$	$2$	2169.d	241.b	$2$	$22$	$22$	$17.320$		None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
2169.2.d.f	$2169$	$2$	2169.d	241.b	$2$	$36$	$36$	$17.320$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2169, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2169, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(241, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(723, [\chi])\)\(^{\oplus 2}\)