Space of modular forms of level 5184, weight 2, and Character 5184.d

• Label: 5184.2.d
• Level: $5184$
• Weight: $2$
• Character orbit: 5184.d
• Rep. character: $\chi_{5184}(2593,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $18$
• Sturm bound: $1728$
• Trace bound: $41$

Defining parameters

Level:	\( N \)	\(=\)	\( 5184 = 2^{6} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5184.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1728\)
Trace bound:			\(41\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\), \(23\), \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5184, [\chi])\).

	Total	New	Old
Modular forms	936	96	840
Cusp forms	792	96	696
Eisenstein series	144	0	144

Trace form

\( 96 q - 96 q^{25} + 96 q^{49}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5184, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5184.2.d.a	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(\zeta_{12})\)	None		✓			5184.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{5}+(-\beta_{3}-3)q^{7}+(-\beta_{2}-3\beta_1)q^{11}+\cdots\)
5184.2.d.b	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(\zeta_{12})\)	None		✓			5184.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{5}+(\beta_{3}-3)q^{7}+(-\beta_{2}+3\beta_1)q^{11}+\cdots\)
5184.2.d.c	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(\zeta_{12})\)	None					576.2.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{5}-3\beta_1 q^{11}-\beta_{2} q^{13}-3 q^{17}+\cdots\)
5184.2.d.d	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(\zeta_{12})\)	None		✓			5184.2.d.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{5}-\beta_{3} q^{7}-\beta_{2} q^{13}-3 q^{17}+\cdots\)
5184.2.d.e	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-2}) \)					576.2.r.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{11}+(-3+\beta _{3})q^{17}+(-\beta _{1}+\cdots)q^{19}+\cdots\)
5184.2.d.f	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(\zeta_{12})\)	None		✓			5184.2.d.f	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta_1 q^{5}+2\beta_{2} q^{11}-3\beta_{2} q^{13}+\cdots\)
5184.2.d.g	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(i, \sqrt{15})\)	None					576.2.r.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+\beta _{2}q^{7}+3\beta _{1}q^{11}-\beta _{3}q^{13}+\cdots\)
5184.2.d.h	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(i, \sqrt{15})\)	None					576.2.r.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}-\beta _{2}q^{7}-3\beta _{1}q^{11}+\beta _{3}q^{13}+\cdots\)
5184.2.d.i	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(\zeta_{12})\)	None		✓			5184.2.d.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta_1 q^{5}-2\beta_{2} q^{11}-3\beta_{2} q^{13}+\cdots\)
5184.2.d.j	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(\zeta_{12})\)	None					576.2.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{5}-3\beta_1 q^{11}+\beta_{2} q^{13}+3 q^{17}+\cdots\)
5184.2.d.k	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(\zeta_{12})\)	None		✓			5184.2.d.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{5}-\beta_{3} q^{7}+\beta_{2} q^{13}+3 q^{17}+\cdots\)
5184.2.d.l	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-2}) \)					576.2.r.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{11}+(3-\beta _{3})q^{17}+(\beta _{1}+\cdots)q^{19}+\cdots\)
5184.2.d.m	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(\zeta_{12})\)	None		✓			5184.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{5}+(-\beta_{3}+3)q^{7}+(\beta_{2}-3\beta_1)q^{11}+\cdots\)
5184.2.d.n	$5184$	$2$	5184.d	8.b	$2$	$4$	$4$	$41.394$	\(\Q(\zeta_{12})\)	None		✓			5184.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{5}+(\beta_{3}+3)q^{7}+(\beta_{2}+3\beta_1)q^{11}+\cdots\)
5184.2.d.o	$5184$	$2$	5184.d	8.b	$2$	$8$	$8$	$41.394$	\(\Q(\zeta_{24})\)	None		✓			5184.2.d.o	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{6} q^{5}-\beta_{3} q^{7}-\beta_{5} q^{11}-\beta_{4} q^{13}+\cdots\)
5184.2.d.p	$5184$	$2$	5184.d	8.b	$2$	$8$	$8$	$41.394$	\(\Q(\zeta_{24})\)	None		✓			5184.2.d.o	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{6} q^{5}+\beta_{3} q^{7}+\beta_{5} q^{11}+\beta_{4} q^{13}+\cdots\)
5184.2.d.q	$5184$	$2$	5184.d	8.b	$2$	$12$	$12$	$41.394$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					576.2.r.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{5}-\beta _{4}q^{7}+(-\beta _{7}-\beta _{9})q^{11}+\cdots\)
5184.2.d.r	$5184$	$2$	5184.d	8.b	$2$	$12$	$12$	$41.394$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					576.2.r.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{5}+\beta _{4}q^{7}+(\beta _{7}+\beta _{9})q^{11}+\beta _{10}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5184, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5184, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1728, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2592, [\chi])\)\(^{\oplus 2}\)