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

\( 96 q + O(q^{10}) \)

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

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

\( S_{2}^{\mathrm{old}}(5184, [\chi]) \cong \)