Space of modular forms of level 2184, weight 2, and Character 2184.bj

• Label: 2184.2.bj
• Level: $2184$
• Weight: $2$
• Character orbit: 2184.bj
• Rep. character: $\chi_{2184}(841,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $14$
• Sturm bound: $896$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2184 = 2^{3} \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2184.bj (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(896\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2184, [\chi])\).

	Total	New	Old
Modular forms	928	80	848
Cusp forms	864	80	784
Eisenstein series	64	0	64

Trace form

\( 80 q - 8 q^{5} - 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2184, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2184.2.bj.a	$2184$	$2$	2184.bj	13.c	$3$	$2$	$1$	$17.439$	\(\Q(\sqrt{-3}) \)	None		✓			2184.2.bj.a	$2$	$0$	\(0\)	\(1\)	\(-4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-2q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2184.2.bj.b	$2184$	$2$	2184.bj	13.c	$3$	$2$	$1$	$17.439$	\(\Q(\sqrt{-3}) \)	None		✓			2184.2.bj.b	$2$	$0$	\(0\)	\(1\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2184.2.bj.c	$2184$	$2$	2184.bj	13.c	$3$	$2$	$1$	$17.439$	\(\Q(\sqrt{-3}) \)	None		✓			2184.2.bj.c	$2$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+(-1+\cdots)q^{11}+\cdots\)
2184.2.bj.d	$2184$	$2$	2184.bj	13.c	$3$	$2$	$1$	$17.439$	\(\Q(\sqrt{-3}) \)	None		✓			2184.2.bj.d	$2$	$0$	\(0\)	\(1\)	\(4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+2q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2184.2.bj.e	$2184$	$2$	2184.bj	13.c	$3$	$2$	$1$	$17.439$	\(\Q(\sqrt{-3}) \)	None		✓			2184.2.bj.e	$2$	$0$	\(0\)	\(1\)	\(6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+3q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2184.2.bj.f	$2184$	$2$	2184.bj	13.c	$3$	$4$	$2$	$17.439$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		✓			2184.2.bj.f	$2$	$0$	\(0\)	\(-2\)	\(-6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots\)
2184.2.bj.g	$2184$	$2$	2184.bj	13.c	$3$	$6$	$3$	$17.439$	6.0.2958147.4	None		✓			2184.2.bj.g	$2$	$0$	\(0\)	\(3\)	\(0\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{3})q^{3}+(1-\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
2184.2.bj.h	$2184$	$2$	2184.bj	13.c	$3$	$8$	$4$	$17.439$	8.0.8548296849.1	None		✓			2184.2.bj.h	$2$	$0$	\(0\)	\(-4\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{3}+(1+\beta _{4}-\beta _{6}-\beta _{7})q^{5}+\cdots\)
2184.2.bj.i	$2184$	$2$	2184.bj	13.c	$3$	$8$	$4$	$17.439$	8.0.\(\cdots\).1	None		✓			2184.2.bj.i	$2$	$0$	\(0\)	\(-4\)	\(4\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{3}+(1-\beta _{2})q^{5}+(1+\beta _{4})q^{7}+\cdots\)
2184.2.bj.j	$2184$	$2$	2184.bj	13.c	$3$	$8$	$4$	$17.439$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓			2184.2.bj.j	$2$	$0$	\(0\)	\(4\)	\(-8\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{5})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
2184.2.bj.k	$2184$	$2$	2184.bj	13.c	$3$	$8$	$4$	$17.439$	8.0.8248090761.1	None		✓			2184.2.bj.k	$2$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{3}-\beta _{5}q^{5}+(-1+\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
2184.2.bj.l	$2184$	$2$	2184.bj	13.c	$3$	$8$	$4$	$17.439$	8.0.4601315889.1	None		✓			2184.2.bj.l	$2$	$0$	\(0\)	\(4\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{5})q^{3}+(\beta _{2}-\beta _{4}-\beta _{6})q^{5}+\beta _{5}q^{7}+\cdots\)
2184.2.bj.m	$2184$	$2$	2184.bj	13.c	$3$	$10$	$5$	$17.439$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓			2184.2.bj.m	$2$	$0$	\(0\)	\(-5\)	\(-6\)	\(-5\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{6})q^{3}+(-1-\beta _{2})q^{5}-\beta _{6}q^{7}+\cdots\)
2184.2.bj.n	$2184$	$2$	2184.bj	13.c	$3$	$10$	$5$	$17.439$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			2184.2.bj.n	$2$	$0$	\(0\)	\(-5\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{6})q^{3}+(\beta _{1}+\beta _{4})q^{5}+\beta _{6}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2184, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2184, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1092, [\chi])\)\(^{\oplus 2}\)