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

• Label: 5184.2.c
• Level: $5184$
• Weight: $2$
• Character orbit: 5184.c
• Rep. character: $\chi_{5184}(5183,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $13$
• Sturm bound: $1728$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 5184 = 2^{6} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5184.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(1728\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	936	100	836
Cusp forms	792	92	700
Eisenstein series	144	8	136

Trace form

\( 92 q - 4 q^{13} - 72 q^{25} + 8 q^{37} - 64 q^{49} - 4 q^{61} - 8 q^{73} + 16 q^{85} + 4 q^{97}+O(q^{100}) \)

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.c.a	$5184$	$2$	5184.c	12.b	$2$	$2$	$2$	$41.394$	\(\Q(\sqrt{-3}) \)	None					144.2.s.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta q^{5}-2\beta q^{7}-3 q^{11}-4 q^{13}+\cdots\)
5184.2.c.b	$5184$	$2$	5184.c	12.b	$2$	$2$	$2$	$41.394$	\(\Q(\sqrt{-3}) \)	None					144.2.s.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{5}-\beta q^{7}-3 q^{11}+5 q^{13}-4\beta q^{17}+\cdots\)
5184.2.c.c	$5184$	$2$	5184.c	12.b	$2$	$2$	$2$	$41.394$	\(\Q(\sqrt{-3}) \)	None					144.2.s.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta q^{5}+2\beta q^{7}+3 q^{11}-4 q^{13}+\cdots\)
5184.2.c.d	$5184$	$2$	5184.c	12.b	$2$	$2$	$2$	$41.394$	\(\Q(\sqrt{-3}) \)	None					144.2.s.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{5}+\beta q^{7}+3 q^{11}+5 q^{13}-4\beta q^{17}+\cdots\)
5184.2.c.e	$5184$	$2$	5184.c	12.b	$2$	$4$	$4$	$41.394$	\(\Q(\sqrt{-2}, \sqrt{3})\)	\(\Q(\sqrt{-1}) \)					324.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{5}+(-2-\beta _{3})q^{13}+(3\beta _{1}+\beta _{2}+\cdots)q^{17}+\cdots\)
5184.2.c.f	$5184$	$2$	5184.c	12.b	$2$	$4$	$4$	$41.394$	\(\Q(\zeta_{12})\)	None					144.2.s.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{5}+\beta_1 q^{7}+\beta_{3} q^{11}-q^{13}+\cdots\)
5184.2.c.g	$5184$	$2$	5184.c	12.b	$2$	$4$	$4$	$41.394$	\(\Q(\sqrt{-2}, \sqrt{3})\)	\(\Q(\sqrt{-1}) \)					1296.2.c.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{5}+(2-\beta _{3})q^{13}+(-\beta _{1}+\beta _{2}+\cdots)q^{17}+\cdots\)
5184.2.c.h	$5184$	$2$	5184.c	12.b	$2$	$8$	$8$	$41.394$	\(\Q(\zeta_{24})\)	None					1296.2.c.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{5}+\beta_{4} q^{7}+\beta_{2} q^{11}-q^{13}+\cdots\)
5184.2.c.i	$5184$	$2$	5184.c	12.b	$2$	$8$	$8$	$41.394$	\(\Q(\zeta_{24})\)	None					2592.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{3}-\beta_1)q^{5}+\beta_{5} q^{7}+(\beta_{7}+2\beta_{6})q^{11}+\cdots\)
5184.2.c.j	$5184$	$2$	5184.c	12.b	$2$	$8$	$8$	$41.394$	8.0.170772624.1	None					36.2.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}-\beta _{6}q^{7}+\beta _{3}q^{11}-\beta _{5}q^{13}+\cdots\)
5184.2.c.k	$5184$	$2$	5184.c	12.b	$2$	$8$	$8$	$41.394$	8.0.5780865024.3	None					324.2.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{5}q^{7}+\beta _{4}q^{11}+\cdots\)
5184.2.c.l	$5184$	$2$	5184.c	12.b	$2$	$16$	$16$	$41.394$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					2592.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}-\beta _{8}q^{7}-\beta _{11}q^{11}+(1+\beta _{5}+\cdots)q^{13}+\cdots\)
5184.2.c.m	$5184$	$2$	5184.c	12.b	$2$	$24$	$24$	$41.394$		None			✓		288.2.s.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(5184, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1728, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2592, [\chi])\)\(^{\oplus 2}\)